Alcohol abuse can lead to various health risks including brain damage, heart diseases, stroke etc. But studies yet not proved any connection of alcohol use with lung cancer.
What is alcohol abuse?Alcohols are organic compounds with OH groups. They are used in beverages as sprits which causes, neurodegeneration and nerve injury. The use of alcohol and further adverse affects is called alcohol abuse.
Alcohol abuse leads to severe damages to almost all parts of the body from brain to digestive system. Alcoholic products interfere with the nerve functions and suppress the excitatory nerve pathway activity causing brain damage and strokes.
Alcohol abuse further causes high blood pressure and damage to the heart valves . However, is is not reported that alcoholic use cause lung cancer. It is mainly caused by smoking. Thus option a is correct.
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Ask Tutor a question about your assignment
The current in each branch of the circuit is 9.5 A and 0 A.
Point B, according to Kirchoff's junction law equation is
i = i₁ + i₂ ......equation 1
Now, according to Kirchoff's Loop law,
Loop 2 is anticlockwise, calculates the current i₂ equation is
21.4 - 50i₂ - 6 - i - 100i₂ = 0
150i₂ + i = 15.4 ......equation 2
Loop 1 is clockwise, calculates the current i₁ equation is
20.5 - 30i₁ - 6 - i - 40i₁ - i₁ = 0
80i₁ + i = 14.5 ........equation 3
substitute equation 1 in equation 3 for the value of i,
81i - 80i₂ = 14.5 .....equation 3
Upon, subtracting equation 3 from equation 2, we get i₂ = 9.5 A
substituting the value of i₂ in equation 3, we get i = 9.5A
Hence on substituting value for i₁, in equation 1 , we get i₁ = 0 A
Hence, the current in each branch of the circuit is 9.5A, 9.5A, 0A
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Which of the following statements is most true regarding the use of testimony on hair samples in courts today?
We may not consider the use of hair samples today because DNA analysis is more modern.
What is DNA?The term DNA refers to the molecule that contains the genetic material of the living things. Hence, we could use the DNA sample to be able to solve very difficult cases. This is because the DNA sample can be able to tell the exact identity of the person that involved,
Before the advent of the DNA, the hair sample was one of the very reliable ways be which evidence could be gathered to solve crimes. Hence; Modern DNA analyses have made testimony using hair samples obsolete.
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Missing parts;
Which of the following statements is most true regarding the use of testimony on hair samples in courts today?
Hair samples are replacing DNA as an easily available, go-to source for identifying suspects
Modern changes in the discipline mean that any police officer can provide testimony on hair samples
Modern DNA analyses have made testimony using hair samples obsolete
There’s solid research that should lead us to be skeptical of testimony based on hair samples
5.12 ** consider a simple harmonic oscillator with period r. let ( f ) denote the average value of any variable f (t), averaged over one complete cycle: 1 f (f)
considering simple harmonic oscillator with period r E=1/2mw²A² , T= 1/4mw²A² V = 1/4mw²A² therefore T=V=E/2.
A model with numerous significant applications in both conventional and quantum mechanics is the harmonic oscillator. It acts as a model for the mathematical analysis of a wide range of phenomena, including elasticity, acoustics, AC circuits, molecular and crystal vibrations, electromagnetic fields, and the optical characteristics of matter. A body is referred to be a linear harmonic oscillator or a simple harmonic oscillator when it oscillates about its location along a linear straight line under the influence of a force that is directed towards the mean location and is proportionate to the displacement at any moment from this location. Periodic motion is best demonstrated by this type of oscillation. The period is completely independent of the initial displacement from equilibrium (amplitude of oscillation). The period is unaffected by how far the cart is moved from its equilibrium location. the greatest displacement from the mean position, is the angular speed of the body rotating around in a circle, and t is the duration.
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a system of diatomic ideal gas contracts from a volume of 4.1 m3 to a final volume of 1.3 m3. if the process proceeds at constant pressure of 148 kpa, calculate the energy in kj transferred by heat, where positive is energy transferred into the system, and negative is energy transferred out of the system.
A system of diatomic ideal gas contracts from a volume of 4.1 m3 to a final volume of 1.3 m3. if the process proceeds at constant pressure of 148 kpa. The energy transferred by heat, where positive is energy transferred into the system, and negative is energy transferred out of the system is(Q)= 1450.4 KJ
What is energy?Energy is a physical term that means if a force is applied on a object and the object move some distance that means there is some energy is generate in that object. It is a vector quantity. It can be measured in Joule.
How can we calculate the energy?To calculate the energy we using the formula,
Q = nCp AT
Or, Q = nCp(T₂-T₁)
Or, Q = nCp[P(V₂ - V₁) /nR] ....eq(1)
Here we are given,
V₁ =Initial volume = 4.1 m³
V₂= final volume = 1.3 m³
Process is isobaric so,
p= Constant pressure= 148 kP = 148 x 10³ P
n = Number of moles = 1
Cp= specific heat at constant pressure.
For diatomic molecule Cp = 7R/2
we know, AT = T₂-T₁
From ideal gas equation
PV = nRT
T = PV/ nR
T₁= PV₁/nR
And T₂ = PV₂/nR
Now to calculate energy = Q in KJ transferred by heat at constant pressure.
Substitute all these values in eq (1)
Q = n(7R/2) [P(V₂ - V₁) /nR]
Or, Q = 7P(V₂ - V₁)/2
Or, Q = 3.5(148 × 10³ P) (4.1- 1.3) m³
Or, Q = 1450.4 x 10³ J ........(P.m3 = J)
Or, Q = 1450.4 KJ
From the calculation we can say that, The energy transferred by heat, where positive is energy transferred into the system, and negative is energy transferred out of the system is(Q)= 1450.4 KJ
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A) assume the object moves with a constant acceleration as it rolls down the incline. write an equation that includes acceleration and quantities that can be measured or obtained from measurements by using the available equipment in the list.
1 point for an equation that includes acceleration and is conceptually relevant to the procedure described in part b.
1 part is earned for stating or implying that the initial speed of the object is 0 when released from the top of the incline.
example response: x = 1/2 at^2
The acceleration of a sphere on an inclined plane can be analyzed to a first approximation ignoring frictional forces. In this case without rotation, the sphere has no torque to rotate so it just slides down the slope with an acceleration of a = g sin θ. The greater the angle, the greater the acceleration of the object. The description for this refers to the component we drew.
As the angle increases the force component parallel to the slope increases, and the force component perpendicular to the slope decreases. Acceleration is the change in velocity divided by the change in time. A car traveling freely up and down a ramp has constant acceleration. The object then accelerates down the inclined surface due to the presence of an unbalanced force. The parallel component of gravity causes this acceleration.
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a typical insulation resistance of equipment rated 480v is . select one: a. 10 m ohms b. 50 megohms c. 100 megohms d. 1,000 megohms
All different kinds of electrical wires and cables are routinely tested by measuring insulation resistance. This test is frequently used as a customer acceptance test in production settings.
This test is frequently used as a customer acceptance test in production settings, with the customer frequently defining the minimum insulation resistance per unit length.
In contrast to a real HIPOT test, the results of the IR Test are meant to provide information on the quality of the bulk insulation material rather than being helpful in identifying specific insulation flaws.
Many wire and cable manufacturers use the insulation resistance test to track their insulation manufacturing processes and identify emerging issues before process variables stray outside of permitted limits, even when it is not needed by the end customer.
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Following your push the ball rolls down the lane at 4. 2m/s. What is the net force on the ball as it rolls down the lane at the constant speed?
The net force on the ball as it rolls down the lane at the constant speed of 4.2 m / s is zero
F = m a
a = v - u / t
F = Net force
m = Mass
a = Acceleration
v = Final velocity
u = Initial velocity
t = Time
u = v = 4.2 m / s
a = 0
F = 0
This is the result of Newton's first law which states that if there is no external force acting ( F = 0 ) on the object, the object will stay at rest if it is at rest or at constant speed if it is already moving.
Therefore, the net force on the ball as it rolls down the lane at the constant speed is zero
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what is the speed of the book when it reaches the hands? (b) if we substituted a second book with twice the mass, what would its speed be? (c) if, instead, the book were thrown down, would the answer to (a) increase, decrease, or remain the same?
Anything thrown from a structure, you have a downward velocity if you throw it down correctly. Additionally, you have little G, thus the ball will keep accelerating. As a result of the acceleration, your final velocity will undoubtedly be much higher.
At the bottom of the structure, a book is currently being dropped; a man is standing nearby with his hands extended in a very linear motion. The height of these arms is also determined, de Unlike this book, which stands at a specific height Big D The weight of this book has increased to two kilograms. two kg. This small D is equivalent to one point five meters on the issue whereas this enormous D is equal to ten meters of wire. seeks to know the speed at which it will reach this person's grasp.
We have a starting energy and a finishing energy. We also have one more energy. We only have gravitational potential energy, after all. What is our final energy, then? The book is falling, so we have kinetic energy, and since Cromwell is not written in it, we have gravitational potential energy. really easy Therefore, we have M g Big D, followed by 1/2 em, the last square, and M g Little T. What should we do next, then? really easy As a result of our velocity solution, the final square's mg big d minus m g tiny d is equal to 1/2.
Therefore, the final square is equal to two times mg big D, minus mg small D, and you merely need to solve for V divide. I divide by an, you square root it, and the result is equal to two mg large D minus two mg little D all over.
Because if you thought about this properly, your speed would increase. You must simply consider anything. anything falls from a structure. If you throw it down correctly, it will move downward at a speed. Furthermore, since you have little G, the ball will keep accelerating. Because it is accelerating, it follows that your final velocity will be much higher.
Both your initial kinetic energy and your gravitational potential energy would be present, as would your final kinetic energy and gravitational potential energy. Because it is at its highest point, you would have a 1/2 M V initial square plus M g Big D and he would have a 1/2 em final square plus M g tiny. +00 It's not a huge D or small D now that it's in their palm. Therefore, the answer would alter. Your speed would actually rise, in my opinion, if you give this some careful thought. You only need to consider anything.
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what is the power of 600 joules of work done in 4 seconds?responses 150 watts 150 watts 240 watts 240 watts 600 watts 600 watts 2,400 watts
150 Watts is the power of 600 J of work completed in 4 seconds.
The rate at which work is completed is referred to as power. It has the following mathematical expression:
[tex]Power = work/time[/tex]
The power can be obtained using the above formula.
From the mentioned query, the following information was observed:
Work = 600 J
Time = 4 s
Power =?
[tex]Power = Work/Time \\Power = 600/4[/tex]
power = 150 watts
Thus, 150 Watts are generated by 600 J of work completed in 4 seconds.
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A 750 resistor in a circuit has a current flowing through it of 2.0 A. What is
the power dissipated by the resistor? (Use P=OVI = /²R= VR)
OA. 300 W
B. 150 W
C. 38 W
D. 450 W
The power dissipated by the resistor is 3000W.
What is power?Electrical power, or (P), in a circuit is a unit of measurement for the rate at which energy is consumed or produced inside a circuit. The energy produced or delivered by an energy source, such as a voltage, is absorbed by the associated load.
In physics, power is referred to as the rate of energy conversion or transfer over time. The unit of power in the SI system, often known as the International System of Units, is the Watt (W). A single joule per second is one watt. Power was formerly referred to as activity in some research. A scalar quantity is power.
The resistor's power dissipation can be computed as P = I²R
here ,
I = 2 A
R = 750
Therefore P= 2² x 750 W
= 3000W
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At a gas is in a container with a constant temperature pressure change cause the volume to decrease based on the relationship between pressure and volume what must happen to the pressure
At constant temperature pressure is inversely proportional to volume, so pressure will increase.
What is temperature and pressure and the relation?Temperature is the measure of degree of hotness and degree of coldness.Pressure is force per unit area and is inversely proportional to volume at constant temperature.Here the gas in a container is at constant temperature and also at constant pressure.So the pressure will increase because the volume is decreasing .Though at constant temperature the pressure of the gas is directly proportional to mole of the gas.But that's not significant here , at constant temperature pressure goes in inverse relation to volume.To know more about pressure visit:
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suppose two children push horizontally, but in exactly opposite directions, on a third child in a wagon. the first child exerts a force of 74.0 n, the second a force of 89.0 n, friction is 8.00 n, and the mass of the third child plus wagon is 23.0 kg.
The wagon and the child inside it make up the system of interest, acceleration equals 0.13 m/s² in the direction of child 1 and Zero acceleration if friction is 15.0 N.
When two things are moved against one another, instant friction results. The motion will be opposed by the friction, who will also be working against it. When an item is in motion and its velocity changes, the concept of acceleration takes place. Friction, which opposes motion, always lowers acceleration. An object and a surface come into contact and cause friction. The features of the surface and the item, as well as whether or not the object is moving, determine its magnitude. Always, friction works in the opposite direction of motion. As a result, friction cancels out some of the force driving motion when it is there. Therefore, there will be less acceleration and net force.
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True or false Condensation occurs with the removal of thermal energy.
true. condensation is when gas converts to liquid. the molecules move slower because of a loss of thermal energy, so it forms liquid
use letter B below to explain what is wrong with the orbital diagram for beryllium
Electronic Configuration:
Normally, the electronic configuration will be written through the atomic number of the particular element. The electrons fill in this accruing to the energy level and orbitals like s, p, d, and f
The atomic number for the Beryllium is 4. So, the electronic configuration of beryllium is
[tex]1s^22s^2[/tex]In option B, the s block has two electrons and both are having an upward spin orientation. This is incorrect, as one must be in the upward orientation and the other will be in the downward orientation
a gun with a muzzle velocity of 100 m/s is fired horizontally from a tower. neglecting air resistance, how far will the bullet fall 1 second later (vertical distance) ? * 1 point a) 5 m b) 50 m c) 100 m d) 490 m e) none of these
option c A gun is fired horizontally from a tower with a muzzle velocity of 100 m/s. The bullet will arrive 100m away and arrive 1 second late if air resistance is ignored.
That is not to argue that there isn't a velocity increase. It absolutely depends on the specific firearm, cartridge, and loading in question. The reason for an increase in velocity is that the pressures are slightly higher, which causes the bullet to move less before engaging the rifling.
However, a significant improvement in accuracy is what many handloads will discover. A smaller distance to the rifling reduces the possibility of any bullet tipping and the variation in breech pressures that exists between different rounds. From round to round, slightly variable pressures can and will be produced even with equal powder loads, down to less than 1/10th of a grain. It's a simple reality.
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A man pulls a crate with a rope. The crate slides along the floor in the horizontal direction (x direction). The man exerts a force of 50 N on the rope, and the rope is at an angle . Describe how the force components change as the angle increases from 0° to 90° and use your graph to explain your answer. Give a detailed explanation of the forces at . Show a sample calculation at one angle for both components.
The 50 N force applied at an angle to the crate may be broken down into horizontal and vertical force components. As the angle created by the rope, e, increases from 0° to 90°, the horizontal component, Fx, drops and the vertical force component, Fy, increases.
What is a component of a force ?The components of a force are the force parts acting in perpendicular directions, horizontal and vertical, that combine to give the specified force.
The direction the crate is sliding = The horizontal, x-direction
The force exerted by the man = 50 N
The angle of the rope
The components of the force are therefore:
Horizontal component, Fx = 50 × cos(8)
Vertical component, F₁ = 50 x sin(0)
The value of cos(e) and sin(e) as the angle the rope makes with the horizontal,
e, increases from 0° to 90° are as follows:
Therefore, the horizontal component of the force exerted by the man, Fx has a maximum value at = 0, and decreases to 0, as increases from 0° to 90°.
The vertical component of the force exerted, Fy, has a minimum value of O at → = 0°, and the value of sin(e) and therefore Fy, increases to a maximum of (sin(90°) 1) 50 N as increases to 90°.
Please find attached the graph showing the components of the force, Fx, and Fy, exerted by the man as the angle formed by the rope increases from 0° to 90°
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Help! A car is traveling at 60 km/h. It accelerates to 85km/h in 5 seconds. What is the acceleration of the car?
A Car is travelling at a speed of 60 km/h and then accelerates to the velocity 85 km/h than acceleration in 5 sec is given by 18000 km/h² .
What is acceleration?Acceleration of body is defined as rate of change of the velocity with respect to the time. Acceleration is a vector quantity it have magnitude as well as direction.
Acceleration = (final velocity - initial velocity )/ time
Acceleration = change in velocity / change in time
Given that in the question that the velocity changes from 60 km/h to 85 km/h in 5 sec =( 0.00138 h ) then the acceleration of the car is given as,
Acceleration of the car = (60 - 85)/0.00138
Acceleration of the car = 18000 km/h²
Acceleration of the car travelling with the velocity 60 km/h to final the velocity 85 km/h in time 5 sec is given by 18000 km/h².
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When we see saturn going through a period of apparent retrograde motion, it means.
In its orbit, Earth is passing Saturn, with both planets on the same side of the Sun.
What is apparent retrograde motion?
When a planet appears to be moving backward relative to other bodies in its solar system when viewed from a certain angle, this is known as apparent retrograde motion. Motion in the same direction as other bodies is referred to as direct motion or prograde motion.
Mars typically looks to be traveling to the left of the stars. Mars, however, moves right in relation to the stars during "retrograde motion" periods. Truth be told, that is only an illusion that lasts for around two years. In reality, Earth is orbiting the Sun and is currently passing past Mars. Mars is only occulted by Earth once every 26 months since it orbits the Sun more closely and moves quicker than Mars. Mars typically moves from west to east in the sky, but when Earth passes in front of it, we see it move from east to west, creating the impression that it is going backward.
Hence, the earth is passing Saturn in its orbit, with both planets on the same side of the Sun.
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What is an ellipse?
an elliptical shape
a perfectly round circle
an undefined shape
Answer: In geometry, an ellipse is a two-dimensional shape, that is defined along its axes. An ellipse is formed when a cone is intersected by a plane at an angle with respect to its base.
Explanation:
a plane circular coil of radius 0.77 m lies in a horizontal plane. it carries a current of 4.38 a. the coil is in a uniform horizontal 1.157-t magnetic field. what is the magnitude of the magnetic torque on the coil? calculate the torque in the units of n.m. write your answer in decimal form with three digits to the right of the decimal point (e.g. 5.374); do not write any units.
The magnitude of the magnetic torque on the coil is 9.435 Nm.
A magnetic field exerts a torque that tries to align the normal vector of a loop of current with the magnetic subject. the size of the torque on a loop
The magnetic torque, τ, skilled by using a unmarried particle of quantity V and domain magnetization Md whose moment is oriented at attitude θ to carried out induction B is given by means of τ=mHsinθ where m=MdV is the magnetic second of the particle.
This is the torque on a modern-wearing loop in a uniform magnetic field. This equation can be proven to be valid for a loop of any form. The loop includes a modern I, has N turns, every of area A and the perpendicular to the loop makes an angle θ with the field B.
Calculation:-
τ = μ×B
= I A B sin90°
= 4.38 × 3.14×(0.77)²× 1.157
= 9.435 N m.
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A motorbike and its rider have a mass of 261 kg. If they experience an acceleration of 4.7 m/s2, what force was exerted on them?
Answer:
1226.7
Explanation:
force=ma
261×4.7=1226.7N
What distance will a car traveling at a speed of 50 km/hr cover in 0.25 hr?
Answer: 12.5
Explanation: 50 x 0.25 = 12.5 km
a 40.0-kg child and an 8.40-kg sled are on the surface of an icy lake 15.0 meters apart. the child exerts a 5.20 n force on the sled towards them via a rope they’ve attached.
Acceleration of the sled is 0.62m/s^2
Acceleration of the child is 0.13m/s^2
They met at 2.6m from the child's initial position
The question is incomplete, the complete question is given below:
a 40.0-kg child and an 8.40-kg sled are on the surface of an icy lake 15.0 meters apart. the child exerts a 5.20 n force on the sled towards them via a rope they’ve attached.(a) What is the acceleration of the sled? m/s2(b) What is the acceleration of the child? m/s2(c) How far from the child's initial position do they meet? m
Part a
Acceleration of the sled:
Mass of sled=8.40kg
Force=5.20N
Acceleration=F/m
=5.2/8.4
=0.62m/s^2
Part b
Acceleration of the child
Mass of the child=40kg
Force=5.20N
Acceleration=F/m
=5.2/40
=0.13m/s^2
Part c
Distance from the child's initial position they met
They accelerate towards each other at =0.62+0.13
=0.75m/s^2
The time to meet is given by:
We use kinematic equation to find this,
s=ut+1/2at^2
u=0m/s^2
a=0.75m/s^2
s=15m
t=?
15 =0*t+ (1/2) (0.75) t^2
15=(1/2)*0.75t^2
t=6.32 sec
The child moves:
s=ut+1/2at^2, u=0, a=0.13, t=6.32
=(1/2) (0.13) 6.32^2
=2.6m
Hence they met at 2.6m from the child's original position
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Yani is speaking to an elementary school class on the importance of good nutrition. Without getting into the breakdown of macronutrients and what they
do, how might Yani BEST advise these children to have a balanced diet?
OA. Stick to meat and dairy only, cutting out carbs.
O B.
Don't ever eat candy, cake, or other junk food.
O c.
Try to have many different colors of foods.
OD.
Stick with raw foods instead of cooked ones.
The best advice Yani can give these elementary school children to have a balanced diet is "Don't ever eat candy, cake, or other junk food".
All the given options are true and correct regarding a balanced diet. But for an elementary school child to understand about a balanced diet, one must not et into the breakdown of macronutrients and what they do.
Option A mentions carbs which is a macronutrient. So it is incorrect. Option C is explaining to eat different types of fruits and vegetables. But it might be interpreted wrongly because even junk foods and candies will look colorful. Option D is not a good diet for a child.
Therefore, the best advice Yani can give these elementary school children to have a balanced diet is "Don't ever eat candy, cake, or other junk food".
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Answer:
Try to have many different colors of foods.
Explanation:
When engineers consider the forces that can act on a structure, they must think about all parts of the structure. Describe three different places on a bridge that would experience very different forces.
Any bridge is subject to three different types of forces: the dead load, the live load, and the dynamic load. The weight of the bridge itself is discussed in the first of these words.
What are the 4 different types of forces?Any of the four fundamental forces in physics—gravitational, electromagnetic, strong, and weak—that control how objects or particles interact as well as how some particles decay—is referred to as a fundamental force, also known as a fundamental interaction.
What primary force is acting on the bridge?Compression and tension are the two main forces that are ever-present on a bridge. A force that compresses or shortens the object it is acting on is known as a compressive force. A force known as tension or tensile force works to stretch or expand the object it is acting on.
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What test may be used to determine if a stain is a blood or not?
Answer:
Kastle-Meyer Color Test is used to determine if a stain is blood or not.
Explanation:
which color is bent the least by prism
The red light is the least refracted by the prism.
How light is refracted by a prism?Each beam of light with a particular wavelength is slowed differently by the glass. Since violet light has a shorter prism wavelength, it is brake more than the longer wavelengths of red light. accordingly, violet light is bent the most while red light is bent prism the least. Prism on dispersion, the light rays with longer wavelengths bend less than ones with shorter wavelengths. Since red has the longest wavelength, it bends the least. prism Among the 7 constituent colors of light, violet light has the least wavelength and hence it deviates the most, and red light having the largest wavelength deviates the least. Hence, prism the required order is violet, indigo, blue, green, yellow, orange, and red.
So we can conclude that in a prism, the red light is less refracted.
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Describe how the amplitude of the oscillations of pendulum could be measured.
(3marks)
To find the amplitude of the oscillations of the pendulum, take newton's second law for rotational systems into consideration.
T = I α
-mg sin∅ = mL² d²∅ / dt²
Rearranging the equation as
d²∅ / dt² + g / L sin∅ = 0
If the amplitude of angular displacement is small enough, so the small angle approximation holds, then the equation of motion reduces to the equation of simple harmonic motion
d²∅ / dt² + g / L ∅ = 0
The simple harmonic solution is
∅(t) = ∅' cos(ωt)
where ∅' = initial angular displacement
and ω = √g/L the natural frequency of the motion.
The time period for one oscillation is
T = 2π / ω = 2π√L/g
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One tank of goldfish is fed fish food once a day. A second tank is fed twice a day, and a third tank is fed food four times a day during a six week study. The weight of each fish is recorded daily.
The dependent variable in the experiment in which the weight of each fish is recorded daily is the fish' weight.
A dependent variable is the variable that cannot be controlled in an experiment. An independent variable is the controllable variable/factor in an experiment.
In this experiment, the amount of food fed and how often the food fed can be controlled. The fat gained by the fish and the weight of fish cannot be controlled.
Therefore, in this experiment the dependent variable is weight of fish.
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Q2. A stone leaves a slingshot horizontally with an initial speed of 15.2 m/s from a
height 1.1 m above the ground. Determine the stone's:
a) total air time
b) maximum height
c) range
d) final velocity
Horizontal
VX =
dx = ?
t = ?
Vertical
dy = -1.1m
v1y =
v2y= ?
a =
t = ?
Answer:
Assume that [tex]g = 9.81\; {\rm m\cdot s^{-2}}[/tex]. Also assume that that the air resistance on this stone is negligible.
The total air time of this stone is approximately [tex]1.5\; {\rm s}[/tex].
The maximum height of this stone is [tex]1.1\; {\rm m}[/tex], same as the height of the slingshot.
The range of this stone is approximately [tex]23\; {\rm m}[/tex].
The final velocity of this stone is approximately [tex]21\; {\rm m \cdot s^{-1}}[/tex].
Explanation:
If the air resistance on this stone is negligible, this stone will accelerate towards the ground with a vertical acceleration [tex]a_{y}[/tex] of [tex]a_{y} = (-g) = (-9.81)\; {\rm m\cdot s^{-2}}[/tex].
At the same time, the horizontal velocity [tex]v_{x}[/tex] of this stone will stay the same during the entire flight: [tex]v_{x} = 15.2\; {\rm m\cdot s^{-1}}[/tex].
The stone was launched from a height of [tex]1.1\; {\rm m}[/tex] above the ground. Therefore, the vertical displacement [tex]x_{y}[/tex] of the stone will be [tex]x_{y} = (-1.1)\; {\rm m}[/tex] when the stone hits the ground.
The initial vertical velocity [tex]u_{y}[/tex] of this stone would be [tex]u_{y} = 0\; {\rm m\cdot s^{-1}}[/tex] since the stone was launched horizontally.
Let [tex]v_{y}[/tex] denote the final vertical velocity of this stone right before landing. Apply the SUVAT equation [tex](v_{y})^{2} - (u_{y})^{2} = 2\, a\, x[/tex] to find [tex]v_{y}\![/tex]:
[tex](v_{y})^{2} - (u_{y})^{2} = 2\, a\, x[/tex].
[tex](v_{y})^{2} = (u_{y})^{2} + 2\, a\, x[/tex].
[tex]\begin{aligned}v_{y} &= -\sqrt{(u_{y})^{2} + 2\, a\, x} \\ &= -\sqrt{0^{2} + 2\, (-9.81) \, (-1.1)}\; {\rm m\cdot s^{-1}} \\ &\approx -14.6908 \end{aligned}[/tex].
(Final vertical velocity [tex]v_{y}[/tex] is negative since the stone is travelling downwards toward the ground.)
Let [tex]t[/tex] denote the duration of this flight. Apply the SUVAT equation [tex]t = (v_{y} - u_{y}) / (a)[/tex] to find [tex]t\![/tex]:
[tex]\begin{aligned} t &= \frac{v_{y} - u_{y}}{a} \\ &\approx \frac{(-14.6908) - 0}{(-9.81)}\; {\rm s} \\ &\approx 1.49753\; {\rm s} \end{aligned}[/tex].
In other words, this stone was in the air for approximately [tex]1.5\; {\rm s}[/tex].
Also because the stone was launched horizontally, the vertical velocity of this stone started at [tex]u_{y} = 0\; {\rm m\cdot s^{-1}}[/tex] and became negative (toward the ground) immediately after.
Hence, this stone would not have travelled upward during the entire flight. The height of this stone would be maximized immediately after the stone was launched: [tex]1.1\; {\rm m}[/tex].
Multiple the horizontal velocity [tex]v_{x} = 15.2\; {\rm m\cdot s^{-1}}[/tex] of this stone by the duration of the flight [tex]t \approx 1.49753\; {\rm s}[/tex] to find the range (horizontal displacement) of this stone:
[tex]\begin{aligned} (\text{range}) &= v_{x}\, t \\ &\approx (15.2\; {\rm m\cdot s^{-1}})\, (1.49753\; {\rm s}) \\ &\approx 23\; {\rm m} \end{aligned}[/tex].
Right before landing, the stone would be travelling with a vertical velocity of [tex]v_{y} \approx (-14.6908)\; {\rm m\cdot s^{-1}}[/tex] and a horizontal velocity of [tex]v_{x} = 15.2\; {\rm m\cdot s^{-1}}[/tex]. Apply the Pythagorean Theorem to find the overall velocity of this stone at that moment:
[tex]\begin{aligned} v &= \sqrt{{(v_{x})}^{2}\, {(v_{y})^{2}} \\ &\approx \sqrt{(15.2\; {\rm m\cdot s^{-1})^{2} + (-14.6908)^{2}}\; {\rm m\cdot s^{-1}} \\ &\approx 21\; {\rm m\cdot s^{-1}} \end{aligned}[/tex].