The reaction is at dynamic equilibrium.

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

3 years ago

Which section of the reaction represents the reactants? A) a B) b C) c D) d

ivann1987 [24]

This question is incomplete, but I can do it for you, considering the equation to be *In its most famous form*:
A+B⇒C+D
A and B here are the reactants, while C and D are the products.
The reactants are generally the input materials in the beginning of any chemical reactions and they usually, if not always, are on the left hand side of the chemical equation. While the products are on the right hand side and are the final output of the chemical reaction.

Hope this helps.

3 0

3 years ago

Read 2 more answers

A major difference between radio waves, visible light, and gamma rays is the ____ of the photons, which results in the different

olga2289 [7]

The sentence can be completed as follows:
"A major difference between radio waves, visible light, and gamma rays is the energy of the photons, which results in the different photon frequencies and wavelengths."

In fact, gamma rays have greater energy than visible light and visible light has greater energy than radio waves. The energy E of a photon is related to its frequency, f, by
 $E=hf$
where h is the Planck constant. We see from this formula that the higher the frequency, the greater the energy. Instead, the wavelength is inversely proportional to the frequency:
 $\lambda= \frac{c}{f}$
where c is the speed of light. Since the frequency is directly proportional to the energy, this means that the wavelength is inversely proportional to the energy.

8 0

3 years ago

Read 2 more answers

a layer of sandstone is in contact with a mass of granite. the sandstone contains small fragments of the granite. which rock is

lara31 [8.8K]

The granite would be older. As millions of years go by, rocks are affected by weathering and erosion. These processes break down rocks and scatter them. Rocks are broken down into sediments, which mix with other layers, which could have been the reason how the layer of sandstone contains the small fragments of granite.

8 0

2 years ago

Which of the following most directly limits the number of organisms in a community?

astraxan [27]

Answer:

It can either be food, mating, or competition with other organisms for resources.

7 0

2 years ago