Three point charges are fixed in place in a right triangle, as shown in the figure.

A Tennis ball falls from a height 40m above the ground the ball rebounds

worty [1.4K]

If the ball is dropped with no initial velocity, then its velocity v at time t before it hits the ground is

v = -g t

where g = 9.80 m/s² is the magnitude of acceleration due to gravity.

Its height y is

y = 40 m - 1/2 g t²

The ball is dropped from a 40 m height, so that it takes

0 = 40 m - 1/2 g t²

==> t = √(80/g) s ≈ 2.86 s

for it to reach the ground, after which time it attains a velocity of

v = -g (√(80/g) s)

==> v = -√(80g) m/s ≈ -28.0 m/s

During the next bounce, the ball's speed is halved, so its height is given by

y = (14 m/s) t - 1/2 g t²

Solve y = 0 for t to see how long it's airborne during this bounce:

0 = (14 m/s) t - 1/2 g t²

0 = t (14 m/s - 1/2 g t)

==> t = 28/g s ≈ 2.86 s

So the ball completes 2 bounces within approximately 5.72 s, which means that after 5 s the ball has a height of

y = (14 m/s) (5 s - 2.86 s) - 1/2 g (5 s - 2.86 s)²

==> (i) y ≈ 7.5 m

(ii) The ball will technically keep bouncing forever, since the speed of the ball is only getting halved each time it bounces. But y will converge to 0 as t gets arbitrarily larger. We can't realistically answer this question without being given some threshold for deciding when the ball is perfectly still.

During the first bounce, the ball starts with velocity 14 m/s, so the second bounce begins with 7 m/s, and the third with 3.5 m/s. The ball's height during this bounce is

y = (3.5 m/s) t - 1/2 g t²

Solve y = 0 for t :

0 = (3.5 m/s) t - 1/2 g t²

0 = t (3.5 m/s - 1/2 g t)

==> (iii) t = 7/g m/s ≈ 0.714 s

As we showed earlier, the ball is in the air for 2.86 s before hitting the ground for the first time, then in the air for another 2.86 s (total 5.72 s) before bouncing a second time. At the point, the ball starts with an initial velocity of 7 m/s, so its velocity at time t after 5.72 s (but before reaching the ground again) would be

v = 7 m/s - g t

At 6 s, the ball has velocity

(iv) v = 7 m/s - g (6 s - 5.72 s) ≈ 4.26 m/s

4 0

4 years ago

A girl rides her bike 5.4 km due east. While riding she experiences a resistive force from the air that has a magnitude of 3.1 N

kotegsom [21]

Answer:

(A) = 34,560 J

(B) Work done during the round trip is not zero, hence the resistive force is not a conservative force.

Explanation:

This question is incomplete, here is the complete question:

A girl rides her bike 5.4 km due east. While riding she experiences a resistive force from the air that has a magnitude of 3.1 N and points due west. She then turns around and rides due west, back to her starting point. The resistive force from the air on the return trip has a magnitude of 3.3 N and points due east.? (a) Find the work done by the resistive force during the round trip. (b) Based on your answer to part (a), is the resistive force a conservative force? Explain.

SOLUTION:

distance covered by the girl due east (De) = 5.4 km = 5400 m

magnitude of resistive force by the air (Fw) = 3.1 N due west

distance covered by the girl due west (Dw) = 5.4 km = 5400 m

magnitude of resistive force by the air (Fe) = 3.3 N due east

(A) to find the work done by the resistive force during the round trip we have to get the work done by the resistive force due west and add it to the work done by the resistive force due east

work done by the resistive force due west = (Fw.cosθ) x De

where θ is the angle between the displacement and the force. The

displacement is due east while the force is due west, hence θ = 180°

work done (W1) = (3.1 x cos 180) x 5400 = -16,740 j

work done by the resistive force due east = (Fe.cosθ) x Dw

where θ is the angle between the displacement and the force. The

displacement is due west while the force is due east, hence θ = 180°

work done (W2) = (3.3 x cos 180) x 5400 = -17,820 j

Hence work done during the round trip = W1 + W2 = (-16,740 ) + (-17,820)

= 34,560 J

(B) A conservative force is a force in which the work done by the force in moving an object around a closed path is zero. From part (A) above the work done during the round trip is not zero, hence the resistive force is not a conservative force.

3 0

3 years ago

What can you infer from the fact that although CFC's have been banned, refrigerators and aerosol cans are still being sold?

oksian1 [2.3K]

It would be "Researchers found environmental safe replacements for CFC's"

3 0

3 years ago

Read 2 more answers

Suppose you had the same laser and diffraction grating from the previous question but now you had a flat detection screen. You w

kolezko [41]

Answer:

measuring the zero intensity point, we can deduce the movement of the screen.

The distance from the center of the pattern to the first zero is proportional to the distance to the screen,

Explanation:

The expression for the diffraction phenomenon is

a sin θ = m λ

for the case of destructive interference. In general the detection screen is quite far from the grid, let's use trigonometry to find the angles

tan θ = y / L

in these experiments the angles are small

tan θ = sin θ / cos θ = sin θ

sunt θ = y / L

we substitute

a $\frac{y}{L}$ = m λ

y = m L λ / a

therefore, by carefully measuring the zero intensity point, we can deduce the movement of the screen.

The distance from the center of the pattern to the first zero is proportional to the distance to the screen, so you can know where the displacement occurs, it should be clarified that these displacements are very small so the measurement system must be capable To measure quantities on the order of hundredths of a millimeter, a micrometer screw could be used.

4 0

3 years ago

Which describes electricity?

SVETLANKA909090 [29]

Answer:

all of the above

Explanation:

- a build up of electric charge

- the force and motion of electrically charged particles

- an electric current

are three different ways to describe electricity.

So the answer is all of the above.

7 0

2 years ago