You are driving your 1800 kg car at 21 m/s over a circular hill that has a radius of 150 m. A deer running across the road causes you to hit the brakes hard while right at the summit of the hill, and you start to skid. The coefficient of kinetic friction between your tires and the road is 0.75.

What is the magnitude of your horizontal acceleration as you begin to slow?

Given:

h = height = 20 ft = 6.096 m

m = 150 pound = 68.0389 kg

time = 15 s

g= 9.8 m/s^2

Potential energy = mgh = (68.0389 ) (9.8 ) (6.096 ) = 4,064.7 J

Work done = 4,064.7 J

Answer:

v = u + at

Explanation:

initial velocity = u = 0

acceleration of the car = a = 7.8 m/s^2

time taken to reach a speed of, v = 6 m/s

hence,

6 = 0 + 7.8 x t

t = 6/7.8

t = 0.77 s

Answer:

This reduces the kinetic energy of the vehicle, slowing it down and causing the temperature of the brakes to increase. Decelerating from very high speeds too quickly can cause a number of problems: The brakes could overheat and the material they are made from could shatter.

Given:

The volume of a helium balloon: 8.89 liters or 0.00889 cubic meters

The density of helium: 0.177 kilograms per cubic meters

The density of the air: 1.29 kilograms per cubic meters

To find:

a) weight of the helium inside the balloon.

b) the buoyant force exerted on the balloon.

c) the net force on the balloon.

d) number of identical balloons needed to lift a child of mass 24.9 kilograms.

Explanation:

a)

The expression for the density of the balloon is:

Rearrange the above expression to find the mass of the helium.

Substitute the values from the given data, we get:

Thus, the mass of the helium is 0.001573 kg.

The weight of an object is the product of its mass and gravitational acceleration. Thus, the weight of helium is

here, g is the acceleration due to gravity.

Substitute the values, and we get:

The weight of helium is 0.001542 Newtons.

b)

The expression for buoyant force is:

here, ρ is the density, g is the acceleration due to gravity and V is the volume.

To find the buoyant force exerted by helium on the balloon, substitute the values for helium in the above equation.

The buoyant force exerted on the baloon is 0.01542 Newtons.

c)

The buoyant force exerted by the balloon is 0.01542 N and it acts in an upward direction. Whereas, the other force acting on the balloon is the force due to gravity, the weight of the balloon. The weight of the balloon is 0.01542 N and is always acts in the downwards direction.

Since the magnitude of buoyant force exerted on a balloon is equal to the weight of the balloon. Both these forces are acting in opposite directions. Thus the net effect will be zero.

Thus, the net force acting on the balloon is 0 Newtons.

d)

For a helium balloon, 1 liter of helium can lift 1 gram of mass.

The mass of the child is 24.9 kg = 24900 grams.

Thus, to lift a child of mass 24900 grams, 24900 liters of helium is required.

Now, one balloon contains 8.89 liters of helium, thus for 24900 liters of helium volume, the number of ballons required will be,

Rearranging above equation to find n, we get

Thus, approximately 2801 helium balloons are required to lift a child of mass 24.9 kg.

Final answer:

a) The weight of helium is 0.001542 Newtons.

b) The weight of helium is 0.001542 Newtons.

c) The net force acting on the balloon is 0 Newtons.

d) Approximately 2801 helium balloons are required to lift a child of mass 24.9 kg.

Answer:

C. Displacement

Explanation:

When an electron moves between the ends of a 9.00-volt battery, the work done on the electron is 1.44 * 10⁻¹⁸ Jouoles; option C

The work done in moving an electron between two points is defined as the product of the potential difference between the points and the charge on an electron.

Mathematically;

where;

ΔV is the potential difference between the points

q is the charge on the electron.

The potential difference between the two points is the work done in moving a unit positive charge from one point to the other in the circuit.

The charge, q on an electron is 1.609 * 10⁻¹⁹ Coulombs.

For the given electron that moves between the ends of a 9.00-volt battery;

ΔV = 9.000 Volts

q =  1.609 * 10⁻¹⁹ Coulombs

Work done = 9.000 * 1.609 * 10⁻¹⁹

Work done = 1.44 * 10⁻¹⁸ Jouoles

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Answer:

1.22 m/s² (3 s.f.)

Explanation:

Draw a diagram modelling the given situation (see attachment).

Given values:

As the pulling force is at an angle to the plane (ground), resolve the force into components parallel and perpendicular to the plane.

Resolving vertically (↑) to find the Normal Reaction, R:

[tex]\begin{aligned}\implies R+82.2 \sin 64^{\circ}&=14g\\R&=14g-82.2 \sin 64^{\circ}\end{aligned}[/tex]

The frictional force takes its maximum value when an object starts to move (or is on the point of moving):

[tex]\boxed{F_{\text{max}}= \mu R}[/tex]

where R is the Normal Reaction and μ is the coefficient of friction.

Using F = μR to find the Frictional Force, F:

[tex]\begin{aligned}\implies F &= 0.3\left(14g-82.2 \sin 64^{\circ}\right)\\ & =0.3\left(14(9.8)-82.2 \sin 64^{\circ}\right)\\& =0.3\left(137.2-82.2 \sin 64^{\circ}\right)\\ & = 41.16-24.66\sin 64^{\circ}\end{aligned}[/tex]

Newton's second law states that the overall resultant force acting on a body is equal to the mass of the body multiplied by the body’s acceleration:

[tex]\boxed{F_{\text{net}}=ma}[/tex]

Resolving horizontally (→) using Newton's second law of motion to find acceleration:

[tex]\begin{aligned}\textsf{Using} \quad F_{\text{net}}&=ma\\\\\implies 82.2 \cos64^{\circ}-(41.16-24.66\sin 64^{\circ})&=14a\\17.0383694...&=14a\\a&=\dfrac{17.0383694...}{14}\\a&=1.21702638...\\a&=1.22\;\sf m/s^2\;(3\;s.f.)\end{aligned}[/tex]

Therefore, the acceleration of the box is 1.22 m/s² (3 s.f.).

The magnification of first lens can be given as,

Here, m1 is the magnification of first lens, v1 is the distance of image from first lens and u1 is the distance of object from first lens.

Substitute the known values in the equation,

The magnification of second lens can be given as,

Here, m2 is the magnification of second lens, v2 is the distance of image from second lens and u2 is the distance of object from second lens.

Substitute the known values in the equation,

The combined magnification of two lenses can be given as,

Substitute the known values,

Thus, the combined magnification of two lenses is 1.5.

The x-component of the vector is determined as -16.24 m.

The x-component of a vector is the vector component measured along x - direction. It is the vector acting in the x-coordinate.

The magnitude of x -component of a vector is given by the following formula as shown below;

Vₓ = V cosθ

where;

Vₓ = 148 m x cos(-96.3)

Vₓ = -16.24 m

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Answer:

Y= -147

X= -16.24

Explanation:

The processes that help Divya and Melissa identify the spicy taste of the chicken sandwiches with sriracha sauce is sensation.

Sensation is the process in which one feels something after being in physical contact with something. As Divya and Melissa eats the chicken sandwiches with sriracha sauce, their senses tells that the food is spicy.

Acculturation is the process in which one adopts and adjusts to a new cultural environment. Homogenization is the process in which two non-soluble liquids are mixed uniformly. Adaptation is the process of changing one's trait to a new environment.

Therefore,  the processes that helps them identify the spicy taste is sensation.

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A. Magnetic moment will be 17.212*[tex]10^{-4} A-m^{2}[/tex].

B. Torque will be 6.024* [tex]10^{-4} N-m[/tex]

C. 9f B = 35 make angle 60°

then T = 25 × 15,×10³× (5.40x8.50) ×10 × 0.35 Sm 60°

5.22x[tex]10^{-4}[/tex]  n-m

of ∅ = 0° t = 0 ∵ sm0 = 0

As it is a Torque NIAB

= Am². Tesla

= N-3.

Rectangular coils have four sides and slightly rounded edges and are generally cheaper to manufacture. Importantly they cannot handle radial forces more effectively than their circular counterparts and most lose their rectangular shape during short circuits. A rectangular coil carrying current is placed in a uniform magnetic field. The direction in which the spool is difficult to rotate.

The motor works on the principle that when a rectangular coil is placed in a magnetic field and an electric current is applied, a force acts on the coil, causing it to rotate continuously. A toroidal transformer is a type of electrical transformer that consists of a toroidal or annular core. Its primary and secondary windings are wound across the surface of the torus core and separated by insulating material. This configuration minimizes flux leakage.

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Answer:

ΔS = 3.5 m

Explanation:

First, apply the 2º Newton's Law to find the resulting acceleration.

∑F = m × a

F = m × a

14 = 32 × a

a = 14 /32 = 7/16

a = 0.4375 m/s²

Then, we must apply the equation of accelerated movement:

ΔS = V₀*t + (1/2)*a*t²

Starting from the rest and using the value of acceleration:

ΔS = 0*4 + (1/2)*(0.4375)*(4)²

ΔS = (1/2)*(0.4375)*(16)

ΔS = 3.5 m

W0e are asked to determine the frequency of a sound given its velocity and wavelength. To do that we will use the following formula:

Where:

Now, we solve for the frequency by dividing both sides by the wavelength.

Now, we substitute the values:

Solving the operations:

Therefore, the frequency is 40 Hz.

No count number what time of the 12 months it's far, the northern and the southern hemisphere will usually revel in a season contrary to the other.

Therefore, if the northern hemisphere has the summer time, then the southern hemisphere will revel in the wintry weather season. When we are saying contrary we additionally suggest that once it's far spring season in  the northern hemisphere, then it's far autumn season in the southern hemisphere.

The most important motive for this phenomenon is the lean of the earth on its axis. Since the earth is tilted slightly, one of the hemispheres will usually get hold of greater and direct rays from the solar. It approach that once the earth is tilted in the direction of the solar, then the northern hemisphere gets direct solar rays that are skilled through us because the summer time.

During this time the southern hemisphere stories the wintry weather season. This phenomenon maintains alternating because the planet revolves across the sun. This summer time lasts for 1/2 of a 12 months, or instead 1/2 of a revolution.

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The area of the small piston, a, is 0.1963 sq in. and the area of the large piston, A, is 6.28 sq in.​ The force applied to the small piston (f)= 31.21 lb that is required to deliver a working force (F)= 1000 lb

Force is a physical quantity that means if some kind of external or internal affair is happen on a object and the object is move a bit that means a force is act on it. Its a vector quantity.

To calculate the force of the small piston f we are using the formula,

p=P

Or, f/a=F/A

Here we are given,

a= The area of the small piston = 0.1963 sq in

A= The area of the big piston = 6.28 sq in.

F= The force of the big piston = 1000 lb.

We have to calculate the force of the small piston = f

Now we put the values in above equation we get,

f / a = F / A

Or, f = a F/A

Or, f = [tex]\frac{0.1963 \times 1000}{6.28}[/tex]

Or, f = 31.21 lb

Now from the calculation we can say that, The force applied to the small piston (f)= 31.21 lb

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Answer:

Vx = 150 * cos 53 = 90.3 m/s     horizontal speed

Vy = 150 * sin 53 = 120 m/s      vertical speed

t1 = 120 / 9.8 = 12.2 sec       time to reach vertical height  (vy = 0 at apex)

H1 = 1/2 g t^2 = 9.8 / 2 * 12.2^2 = 729 m    height risen above cliff

729 + 405 = 1134 m      total height above striking point

H = 1/2 g T^2          where T is time to fall 1134 m

T = (2 * 1134 / 9.8)^1/2 = 15.2 sec

T + t1 = 15.2  + 12.2 = 27.4 sec total time in air

Sx = Vx * 27.4 = 90.3 * 27.4 = 2470 m   total horizontal distance

Answer:

Kinetic energy

Explanation:

Kinetic energy of an object is directly proportional to the square of its speed (or velocity). An increase in speed will increase the kinetic energy.

We will have that the value will be:

The age of the Universe is  13.8 ± 0.1 billion years.

The ‘hubble constant, h0’ is used to determine the size of the universe. It is a  measurement that is used in describing the universe's expansion. It was a constant introduced by Edwin Hubble. He found out that the farther the distance of the galaxies from the Earth, the faster they would appear to be moving.

One of the most important numbers in cosmology Hubble's constant because it is needed to estimate the size and age of the universe which is  13.8 ± 0.1 billion years.

The age of the universe using Hubble's constant which is  13.8 ± 0.1 billion years.

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Given that the initial velocity is u = 25 m/s.

We have to find the final velocity and time at its maximum height.

First, we need to find the maximum height.

Here, g = 9.81 m/s^2 is the acceleration due to gravity.

Substituting the values, the height will be

(a) Let the final velocity be v.

The formula to calculate final velocity is

Substituting the values, the final velocity will be

(b) The time taken can be calculated by the formula,

Thus, the final velocity is 24.49 m/s and time is 0.051 s

The time taken for the javelin thrown at 28.5 m/s from flat ground at a 43.2 degree angle to reach the maximum height is 2.0 s

From projectile motion, we understand that the time taken to reach maximum height is given as:

t = uSineθ / g

Where

Now, using the above formua, we can obtain the time taken for the javelin to reach the maximum height as follow:

Initial velocity (u) = 28.5 m/s

Angle of projection (θ) = 43.2 degrees

Acceleration due to gravity (g) = 9.8 m/s²

Time taken to reach the peak (t) = ?

t = uSineθ / g

t = (28.5 × Sine 43.2) / 9.8

t = 2.0 s

Thus, the time taken to reach maximum height is 2.0 s

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Given

Initial speed, u=45 m/s

Acceleration

Time taken, t=4 sec

To find

The final speed

Explanation

Let the speed he be going in be v

Thus,

Conclusion

The velocity he is going in is 13 m/s.

Increasing his acceleration will impact his velocity and rate of displacement covered in that as the speed increases due to the increased rate of acceleration, the rate of air resistance also increases.  

Air resistance is a force created by air. When an item moves through the air, the force operates in the opposite direction.

When a diver descends, the force of air resistance acts to counteract the force of gravity. As the skydiver falls faster and faster, the quantity of air resistance grows until it equals the magnitude of gravity's force.

A balance of forces is achieved when the force of gravity equals the force of air resistance, and the skydiver no longer accelerates. The skydiver reaches what is known as terminal velocity.

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Answer:

4.6/4.5 billion years ago

Explanation:

The maximum quantity of repetitions that the athlete could complete with their current level of energy was 229 for such a workout.

Energy efficiency is the ratio of input power to energy output. As just a result, a cookie contains 54.0 kcal in calories. An athlete utilizes the 54.0 kcal in just this cookie for input energy.

The following formula could be employed to measure efficiency:

Energy intake minus power generated is efficiency.

Efficiency = output energy / input energy

After rearrangement above equation.

output energy = efficiency × input energy

Put the given data in above equation.

Output energy = 0.25 × 54 kcal = 13.5 kcal.

Again for power capacity, the lifting exercise was already carried out n times. The source of total output energy is mgh within the form of electromagnetic potential.

So, Energy per repetition = mgh

Where, m will  represent mass g will represent gravity h is height.

By entering the data provided above.

Energy per repetition = 103 kg × 9.8 m/[tex]s^{2}[/tex] × (2.45 × 0.1m)

Energy per repetition= 247.303 J

Energy per repetition =  0.059 kcal.

So, quantity of repetitions = overall output energy / energy per repetition

quantity of repetitions = 13.5 kcal / 0.059 kcal

quantity  of repetitions will be equal to 229 repetitions.  

Therefore, the quantity of repetition would be be 229.

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Answer:

First you must find the kinetic energy that aman use to push her;So you can find the speed that she recoil

We can fulfill the need of humanity by providing them jobs, resources, clean water, good energy, and electricity and by providing many facilities.

We can sustain our need for humanity in many ways which are given below.

First of all, we need to decrease the rate of poverty and hunger to make humanity prosperous. We should provide jobs for those people who are free. We should provide good hospitals and a well-planned health system. We should provide a good and quality education system for the improvement of humanity. Provide clean water and make ways for sanitation. We should provide affordable and clean energy to humanity which should be cheap but not expensive. We should work decently together and provide resources for economic growth. We should sustainably develop our countries because developing involves satisfying the needs of the present population without endangering the capability of the future population to satisfy its own needs.

So we can conclude that providing jobs, resources, clean water, good energy, and electricity, and many facilities to humans is the help of humanity.

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The output force of a hydraulic lift is given by:

In this case we need to lift a patient of mass 82 kg, that means that the lifting force has to be equal to:

Now that we know that we plug the values given, in this case we have:

Therefore the area of the effort piston is 0.022 squared meters (rounded to three decimal).

We know that the components of any vector along the x and y axes are given by:

In this case we know the tha magnitude of the vector is 6.96 m/s; we also know that the angle from the x-axis to the vector is 51.5° (the sum of angles θ and the 26.5° angle); then we have:

Therefore, the components of the vector are: