The magnitude and direction of Ima's resultant displacement is 83.86 m and 30.8⁰ respectively.
What is the resultant displacement?The magnitude of Ima's resultant displacement is calculated as follows;
When she returns, her new position, a = 43 m east
Final position, b = 72 m north
Resultant displacement, d = √a² + b²
d = √(43² + 72²)
d = 83.86 m
The direction of the resultant displacement is calculated as follows;
tan θ = 43 / 72
where;
θ is the direction of the displacement obtained by forming right triangle from the initial and final positiontan θ = 0.597
θ = arc tan(0.597)
θ = 30.8⁰
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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
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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if a radioactive isotope emits 6000 alpha particles in 10 minutes, what is its activity in bequerels?
The radioactivity of the isotope in becquerels is 10 decay/s.
What is radioactivity?
Radioactivity is a phenomenon exhibited by radioactive elements or isotopes by emitting energy and subatomic particles spontaneously.
The radioactivity of a radioactive element or isotope in becquerels is denoted by decay per second.
The radioactivity of the isotope in becquerels is calculated as follows;
Bq = decay / time
decay = 6000 alpha particlestime = 10 minutes = 10 mins x 60 s/min = 600 secondsBq = 6000 / 600
Bq = 10 decay/s
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a 100 kg crate is being pulled across the floor at a constant velocity with a rope that makes an angle of 40 degrees to the horizontal. if the force applied is equal to 300 n, what is the force of friction acting on the box
4. A certain microwave has a wavelength of 0.032 meters. Calculate the frequency of this microwave.
The frequency of this microwave is 9.375 x 10^9 Hz
The frequency of a certain microwave having a wavelength of 0.032m will be 9.375 x 10^9 Hz.
Let:
'v' be the velocity of EMW; v = c 'f' be the frequency of EMW'λ' be the wavelength of EMW; λ = 0.032mUsing the relation between frequency and wavelength:
v = f.λ
c = f(0.032m)
3 x 10^8m/s = f(0.032m)
f = 3 x 10^8/0.032
f = 9.375 x 10^9 Hz
Electromagnetic Waves always travel at the speed of light. Electromagnetic Waves possess both electric and magnetic fields aligned perpendicularly to each other.
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1. An object has a velocity of 3 m/s and a mass of 12 kg.
What is its momentum?
Answer:
Calculate its momentum. Solution:
Given,
Mass of an object (m)=12kg
Velocity (v)=3m/s
then,
p=36kg m/s
Explanation:
while finding momentum ,we should use the formula p=mv
Define SI unit of force. A force of 8N acting on a body changes its velocity uniformly from 2 m/s to 5 m/s in 20s. Calculate the mass of the body.
Answer:
si unit of force is Newton or dyne
Why is speed the magnitude of velocity?
Yes, Speed is the magnitude of its velocity.
What is speed?
velocity is a vector, and Speed is a scalar (just a number). Whereas a velocity has both a direction and a magnitude. As I said, the magnitude of the velocity is known as the speed.
A moving object's speed is the distance it travels in a given length of time. The average speed of an object in a given time is equal to the distance traveled divided by the time. The distance traveled by an object per unit of time is also known as its speed. When an object's speed changes, it becomes faster or slower. Acceleration occurs when the speed of an object increases. Deceleration, or negative acceleration, occurs when an object becomes slower as its speed drops.
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1. Which pair of charges experiences the weakest electrostatic force?
In order to compare the eletrostatic forces, let's calculate each one using the formula:
[tex]F=k\frac{q_1q_2}{r^2}[/tex]Where k = 9 * 10^9, q1 and q2 are the charges and r is the distance between them.
So we have:
[tex]\begin{gathered} q_1=3\cdot10^{-6},q_2=5\cdot10^{-6},r=2\colon \\ F=9\cdot10^9\cdot\frac{3\cdot10^{-6}\cdot5\cdot10^{-6_{}}}{2^2} \\ F=0.03375 \\ \\ q_1=3\cdot10^{-6},q_2=3\cdot10^{-6},r=2\colon \\ F=9\cdot10^9\cdot\frac{3\cdot10^{-6}\cdot3\cdot10^{-6_{}}}{2^2} \\ F=0.02025 \\ \\ q_1=3\cdot10^{-6},q_2=3\cdot10^{-6},r=3\colon \\ F=9\cdot10^9\cdot\frac{3\cdot10^{-6}\cdot3\cdot10^{-6_{}}}{3^2^{}} \\ F=0.009 \\ \\ q_1=5\cdot10^{-6},q_2=5\cdot10^{-6},r=3\colon \\ F=9\cdot10^9\cdot\frac{5\cdot10^{-6}\cdot5\cdot10^{-6_{}}}{3^2} \\ F=0.025 \end{gathered}[/tex]So the weakest force is the one in the third case (bottom left option): charges of -3 uC and +3 uC, and distance of 3 meters.
Which of the following would be a typical application of gamma radiation?
Killing cells and organisms
Producing fluorescence
Heating objects
Transmitting signals between Earth and space
Electromagnetic radiation with the highest energy and shortest wavelength is a gamma ray. When radioactive atomic nuclei disintegrate, gamma rays are generated.
Explain about Gamma radiation?Gamma radiation causes atoms to lose their electrons. As a result, they are classified as ionizing radiation. Studies have shown that radiation can damage DNA, and that this damage can lead to cancer.
In certain cases, extreme exposure can cause cancer or even death. Some tiny microorganisms (bacteria, archaea, and fungi, together referred to as "microbes") have evolved radiation tolerance, despite the fact that gamma radiation can be extremely deadly for humans.
It is common practise to utilise gamma radiation to destroy live things like cells and organisms.
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Which of the following is a reason that the interior of the Earth is HOT?
there will be an image below but if you dont already know, dont answer.
The option that is a reason that the interior of the Earth is hot is option C: Leftover heat from formation.
Which of the following is a reason that the interior of the Earth is hot?The heat from when the planet formed and the heat from radioactive element decay are the two main causes of the extremely heated interior of Earth.
Note that the Earth's interior is warm because the accretion process, which created Earth, produced a lot of heat. Through the course of geologic time, radioactive decay of unstable isotopes has supplied more heat (heat is a byproduct of the decay process). Only the outer core is heated enough to be above the melting point for material of that composition under that level of pressure, making molten rock or magma extremely uncommon in the interior of the earth.
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What is the marginal cost of increasing production from 5,000 units to 6,000 units?
It is to be noted that the marginal cost of increasing production from 5,000 units to 6,000 units, given the information provided, is: "$0.10" (Option D)
What is Marginal Cost?The marginal cost in economics is the change in total cost that occurs when the amount produced is increased or the cost of producing more quantity.
Mathematically, it is expressed as:
MC= ΔC/ ΔQ
Where:
MC = marginal cost
ΔC = change in cost; and
Δ Q = change in quantity
The solution is derived as follows:
Given that:
Total Cost = Fixed cost + Variable cost
Where the problem is defining the marginal cost of upping production from 5000 units to 6000 units.
In the attached table, the Second Row and Third Row respectively indicate increasing production from 5000 units to 6000 units.
In the Second Row, where the number of employees is 20, the output is 5000 units and the Total cost is $2200
Since Total cost = Fixed cost + Variable cost
Therefore, Total cost = $2000 + $200 = $2200
In the Third Row, when the number of employees is 30, the output is 6000 units, and the Total cost is $2300
hence the Total Cost = $2000 + $300 = $2300
So, Marginal Cost =
Change in total cost/change in output units
Where change in Total cost
= Third Row total cost - Second Row total cost
= $2300 - $2200
= $100
and where Change in output units
= Third Row output units - Second Row output units
= 6000 units - 5000 units
= 1000 units
It is verified that the change in total cost is $100 and the change in output units is 1000 units.
Hence, the Marginal cost is:
MC - Change in total cost / Change in output units
= $100 / 1000 units
= $0.10
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Full Question:
See attached image
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:
In three to five sentences, explain how you would conduct an experiment to investigate the relationship between the applied force and the displacement of the spring, and describe its expected results.
Hooke's law states that the applied force F equals a constant k times the displacement or change in length x.
What is Hooke's law?
The force necessary to extend or compress a spring by a certain distance scales linearly with respect to that distance, according to Hooke's law, an empirical law in physics.
Hooke's Law is a principle of physics that states that the that the force needed to extend or compress a spring by some distance.
F = K.x
A straight line passing through the origin can be drawn by plotting the spring's stretch versus the weight that has been applied to the hanger. This implies that a spring's extension is inversely proportional to the force used to stretch it.
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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 plate of cookies and mug of milk are pushed across a smooth table with the same force. The mass of the plate of cookies is 222 times the mass of the mug of milk. Assume that friction is negligible.
How do the objects' accelerations compare?
Answer:The two objects have different amounts of acceleration due to the mass of the two objects being different
Explanation: The mass will affect acceleration. The higher the mass, the slower the acceleration. The formula for acceleration is a = f/m or acceleration = force divided by mass. The acceleration is faster for the milk glass and slower for the plate with cookies because the plate with cookies has a higher mass than the glass of milk.
Answer:
Explanation:
Given:
m₁ = m - Mass of milk mug
m₂ = 222·m₁ = 222·m - Mass of a plate of biscuits
F₁ = F₂ = F
________________
a₂ / a₁ - ?
2 Newton's law:
a = F / m
a₁ = F / m₁ = F / m
a₂ = F / m₂ = F / (222·m)
a₁ / a₂ = (F·222·m) / (F·m) = 222
The acceleration of a mug of milk is 222 times the acceleration of a bowl of cookies
How is a mitochondria and a generator alike
All human cells contain mitochondria, which function as the cell's main "power generator" by transforming energy from food into a form the cell can use. Mitochondria are found in the cytoplasm of all human cells.
How do a generator and a mitochondria compare?
A little DNA strand that functions as a second human genome is also present in them. Additionally, they have a small DNA strand that functions as an additional human genome. Nutrients get into the bloodstream after being broken down.The nutrients can be utilized as fuel or raw materials.Adenosine triphosphate, or ATP, is the major energy source for all of our cells and it is produced by the mitochondria.Our cells include tiny organelles called mitochondria.Consider them the cell's energy producers.The Krebs Cycle, also known as the citric acid cycle, is a mechanism by which mitochondria make ATP, which is used by all cells for energy.Although ATP only exists in minute amounts in each cell, the body can use its entire weight in ATP every day due to its importance as an energy source.Oxygen is the second important component in the process because mitochondria use oxidation (also known as cellular respiration) to produce the energy cells need to function.We need to breathe in order to replenish our bodies' oxygen supply and exhale in order to get rid of carbon dioxide, which is a byproduct of oxidation, because it is produced during the process of cellular respiration. Although ATP only exists in minute amounts in each cell, the body can use its entire weight in ATP every day due to its importance as an energy source.Oxygen is the second important component in the process because mitochondria use oxidation (also known as cellular respiration) to produce the energy cells need to function.We need to breathe in order to replenish our bodies' oxygen supply and exhale in order to get rid of carbon dioxide, which is a byproduct of oxidation, because it is produced during the process of cellular respiration.
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A book of mass 0.4 kg is pushed to the left across a table with a force of 2.4 N. Kinetic friction provides a force of magnitude 0.8 N.
What is the net force acting on the book? Include magnitude and direction. N (answer format example -4 or +4)
(normal force is 3.92 N)
!!!!!!!! PLEASE HELP
-1.6 N
Split the forces into those in the x-direction and those in the y-direction. Since the book is not accelerating upward or downward, the net force in the y-direction is zero. Add the two forces in the x-direction (applied force and kinetic friction). This is the net force.
See details:
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:
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:
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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what is gravitational potential and what is the formula for it
Here is defination of gravitational potential.
gravitational potential energy is the energy possessed or acquired by a object due to a change in it position when it is present in a gravitational is field. In the simple term it can be said to that energy is an gravitatonal potential energy that is related to gravitational force or to gravity.
Formula -
The equation for gravitational potential energy is-
⇒ GPE = m⋅g⋅h
Where-
m is the mass in kilograms of
g is the acceleration due to the gravity (9.8 on Earth)
h is the height above the ground in meter.
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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 gauge pressure is required in the city water mains for a stream from a fire hose connected to the mains to reach a vertical height of 16.0 m ? (assume that the mains have a much larger diameter than the fire hose.)
Gauge pressure required in city water mains for a stream is 147,150 Pa
What is the Bernoulli's theorem for pressure?In fluid mechanics, Bernoulli's principle states that an increase in fluid velocity occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy. This principle is named after the Swiss mathematician Daniel his Bernoulli published it in his 1738 book Fluid Mechanics.
According to the Bernoulli's Equation:
P₁ + ρgy₁ + ([tex]\frac{1}{2}[/tex])ρv₁² = P₂ + ρgy₂ + ([tex]\frac{1}{2}[/tex])ρv₂²
where, y₁ = initial height
y₂ = final height
Initial height is 0 meters and final height is 15 meters.
The problem states that the mains have a much larger diameter than the hose, so v₁ = 0
Once our water reaches a 15 m. altitude, it stops going anymore higher. Therefore, v₂ also be 0.
P₁ = P₂ + ρgy₂
Since, we are solving for gauge pressure, we can assume that the pressure at the top of our column of water is zero.
P₁ = ρgy₂
P₁ = 1000 × 9.8 × 15
P₁ = 147,150 Pa
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A car on the freeway is traveling north at 55 mph on a straight and flat part of the road.
The mass of the car is 1460 kg. The engine is pushing the car forward with a force of
760 N. while the drag on the car is 530 N.
a. Make a free body diagram (FBD) of the car. Label all the forces.
b.Find the weight, Fe. of the car.
C.Calculate the net force on the car. Include magnitude and direction.
The weight of the car is 14308 Newtons and the net force acting on it is 230 N. The free body diagram is attached with the answer.
What is Drag?A drag is force that opposes the motion of an object by acting in the direction opposite to its motion.
Given is a car on the freeway that is traveling north at 55 mph on a straight and flat part of the road. The mass of the car is 1460 kg. The engine is pushing the car forward with a force of 760 N. while the drag on the car is 530 N.
PART - A
The free body diagram is attached with the answer. The following equations will help in mathematical analysis.
F[engine] - F[drag] = ma
a = {F[engine] - F[drag]}/m
and
W = N = mg
PART - B
The weight of the car can be calculated as follows -
W = mg = 1460 x 9.8 = 14308 Newton
PART - C
Net force on the car [F] = Force provided by engine {F[E]} - drag force {F[D]}
F = 760 - 530 = 230 N
The direction of force is towards north.
Therefore, the weight of the car is 14308 Newtons and the net force acting on it is 230 N. The free body diagram is attached with the answer.
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helpppppppppppppppp
A light year is the amount of time it takes for light from the Sun to reach the Earth.
True
False
The ozone layer is important to human life because it protects people from:
microwaves.
gamma rays.
ultraviolet light rays.
None of the choices are correct.
UVA and UVB rays can cause skin damage and skin cancer.
True
False
Which of the following chemicals destroys the ozone layer?
CFCs
gasoline
hydrogen
All of the choices are correct.
The Milky Way is 100,000 light years in size.
True
False
All stars die out after becoming white dwarfs.
True
False
Black holes:
are the brightest objects in space.
are the most well understood objects in space.
pulse in a regular pattern.
None of the choices are correct.
Answer:
Highlighted words are the correct answer
A light year is the amount of time it takes for light from the Sun to reach the Earth.
True
False, a light year is the length light travels in a year
The ozone layer is important to human life because it protects people from:
microwaves.
gamma rays.
ultraviolet light rays.
None of the choices are correct.
UVA and UVB rays can cause skin damage and skin cancer.
True
False
Which of the following chemicals destroys the ozone layer?
CFCs
gasoline
hydrogen
All of the choices are correct.
The Milky Way is 100,000 light years in size.
True
False
All stars die out after becoming white dwarfs.
True
False
Black holes:
are the brightest objects in space.
are the most well understood objects in space.
pulse in a regular pattern. - only some pulse in a regular pattern though
None of the choices are correct.
A 75-N box rests on a perfectly smooth horizontal surface. The minimum force need to start the box moving
is
A) 7.5 N. B) 75 N.
C) 750 N. D) any horizontal force greater than zero.
Here, if take it that you mean "perfectly smooth" to mean that there is no friction. If that is the case, then the box begins to move whenever there is a net horizontal force acting on it. (D) It goes without saying that the force increases as the box accelerates.
An external force is an agent that has the power to alter the resting or moving condition of a body. It has a direction and a magnitude. The application of force is the location at which force is applied, and the direction in which the force is applied is known as the direction of the force.F = ma
Where, F is the force on the box and m is the mass of the box and a is the acceleration.
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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].
How does changing the mass of an object in the system's acceleration when a constant force is applied?
When a constant force is applied, an increase in the mass of an object decreases its acceleration and vice versa.
What is the relationship between the force, mass, and acceleration of an object?The mass of an object is the quantity of matter present in the object.
Force is a push or pull agent that causes a change in the motion or state of rest of an object.
Acceleration of an object is the change in velocity with time of the object.
The relationship between the force, mass, and acceleration of an object is given below:
Force = mass * accelerationMass = Force / accelerationAcceleration = Force / massFrom the above formulas, it can be seen that mass and acceleration have an inverse relationship such that as one increases, the other decreases, and vice versa.
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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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