Ball bouncing in Zero gravity

[robax25]

1. Problem Statement
An astronaut is playing with a ping pong paddle and ball in zero gravity.
The astronaut is 12m from a flat wall and floating toward it at 4m/s .
A ping pong ball bounces back and forth between his paddle and the wall at 11m/s.
Eventually, the astronaut reaches the wall and traps the ball against it.

1)how long does it take the Astronaut to reach the wall?
Ans: 3s.
2) Through what distance does the ball travel during this process in m?

3) If the bounce lasts 25ms. what is the average acceleration of the ball m/s²?

Homework Equations

Height h=ar^(n)
a= first amplitude ,
r=second amplitude
n=number of bounce...1,2,3,4,...

The Attempt at a Solution

t=X/V so time is 3s.

relative velocity=11m/s-4m/s=7m/s

 

[gneill]

Instead of trying to calculate and sum the distances of each individual bounce, what do you know about the average speed of the ball and the total time it is in motion?

 

[robax25]

Average speed of the ball is 11m/s and total time in motion is 3s

 

[gneill]

Average speed of the ball is 11m/s and total time in motion is 3s

Yes, so what distance does it cover in that time?

 

[robax25]

12m

 

[gneill]

12m

How did you calculate that?

 

[robax25]

x=vt so 33m

 

[gneill]

x=vt so 33m

Yes, much better

 

[robax25]

Yes but it is not the right answer. We need to consider relative velocity because Astronaut and ball both are moving.
relative velocity= 11-4=7m/s

x=7m*3s=21m.

 

[gneill]

Yes but it is not the right answer. We need to consider relative velocity because Astronaut and ball both are moving.
relative velocity= 11-4=7m/s

x=7m*3s=21m.

Then I submit that the "right answer" isn't correct. The ball is moving at 11 m/s for three seconds.

Besides, sometimes the ball is moving away from the astronaut, sometimes towards him. There would be different relative velocities for the two cases.

 

[robax25]

Yes you are right. I am wrong. However, why there is two different relative velocities. yes, first case, the ball is moving away and second case ball is moving towards him but the velocity is constant for Astronaut(4m/s) and ball (11m/s). For my point of view, there can be two relative velocities because of displacement.

 

[gneill]

Yes you are right. I am wrong. However, why there is two different relative velocities. yes, first case, the ball is moving away and second case ball is moving towards him but the velocity is constant for Astronaut(4m/s) and ball (11m/s). For my point of view, there can be two relative velocities because of displacement.

What precisely do you mean by relative velocity? The relative velocity between what two things?

An observer in the rest frame of the spacecraft would judge the astronaut to have a constant velocity, but would see the ball's velocity changing between +11 m/s and -11 m/s.

 

[mattt]

For fun, be aware that if the bounces were instantaneous, then the ball would bounce an infinite number ot times (in this mathematical model), but if we decide that each bounce requires a non-zero finite amount of time (it would be a different model), then the number of bounces would be finite, and you can calculate that exact finite number of bounces (just in case you want to have some fun).

 

[haruspex]

if we decide that each bounce requires a non-zero finite amount of time (it would be a different model), then the number of bounces would be finite

If the sum of the series of bounce times converges then there could be infinitely many.

 

[mattt]

If the sum of the series of bounce times converges then there could be infinitely many.

Yeah, I mean, if each bounce has the same non-zero duration, then there can only be a finite number of bounces, but yes, if we allow the duration of the bounces to be smaller and smaller in an appropriate way, then yes, there could still be an infinite number of bounces.

 

[haruspex]

Yes you are right. I am wrong. However, why there is two different relative velocities. yes, first case, the ball is moving away and second case ball is moving towards him but the velocity is constant for Astronaut(4m/s) and ball (11m/s). For my point of view, there can be two relative velocities because of displacement.

(Somewhat belatedly) The question implies the ball's speed is constant. In practice, it slows a little each time it bounces from the wall because some momentum is transferred to the spacecraft .
Likewise, the astronaut has to hold the paddle nearly still in the reference frame of the spacecraft during each contact in order to get the ball back up to 11m/s in the spacecraft 's frame, and no more.
And then there is the slowing of the astronaut. Is it clear that the astronaut can reach the wall?

 

[willem2]

(Somewhat belatedly) The question implies the ball's speed is constant. In practice, it slows a little each time it bounces from the wall because some momentum is transferred to the spacecraft .
Likewise, the astronaut has to hold the paddle nearly still in the reference frame of the spacecraft during each contact in order to get the ball back up to 11m/s in the spacecraft 's frame, and no more.
And then there is the slowing of the astronaut. Is it clear that the astronaut can reach the wall?

This is a variant of the well-known "Bird and train problem" (bird flying back and forth between 2 approaching trains. With a bird there is no problem keeping the speed constant.

I think the astronaut can reach the wall. There is a minimum time given for a bounce, so there can only be a finite number of bounces. and only a finite amount of momentum can be transferred.
If there was no minimum bounce time, there's no limit to the number of bounces, and since a constant amount of momentum gets transferred every time, the astronaut will stop and reverse direction.

BTW 25 ms is much too long for the bounce time. The ball travels 275 mm in that time. the paddle/walls are apparently very elastic. This makes the total distanced traveled by the ball unclear, since we don't really know how much it travels during a bounce.

 

[Delta2]

I think for questions 1) and 2) the problem wants us to assume that

• the bounce time is zero
• the momentum transfer from the ball to the spaceship is negligible
• the momentum transfer from the ball to the astronaut is also negligible

 

[G9raz]

If the bounce lasts 25ms. what is the average acceleration of the ball m/s²?
Can anybody solve this?
which equation to use?
What will be the v_f, time, displacement and v_i?

 

[Delta2]

If the bounce lasts 25ms. what is the average acceleration of the ball m/s²?
Can anybody solve this?
which equation to use?
What will be the v_f, time, displacement and v_i?

I think we should use $$a=\frac{\Delta v}{\Delta t}$$, with $\Delta t=0.025$ , $\Delta v=11-(-11)$.

 

[G9raz]

I think we should use $$a=\frac{\Delta v}{\Delta t}$$, with $\Delta t=0.025$ , $\Delta v=11-(-11)$.

Thank u very much
I'm very grateful

 

[G9raz]

10 The engines of a rocket sitting on the ground fire to accelerate the rocket at 3.5\,\mathrm{m/s^2}3.5m/s2 until it reaches an altitude of 1.2\,\mathrm{km}1.2km. At that point, the engines fail and the rocket is in free fall.

What height does the rocket reach in \mathrm{m}m? Assume a constant acceleration of gravity of 9.8\,\mathrm{m/s^2}9.8m/s2 even at these high altitudes.
Can anybody solve this too?

 

[haruspex]

10 The engines of a rocket sitting on the ground fire to accelerate the rocket at 3.5\,\mathrm{m/s^2}3.5m/s2 until it reaches an altitude of 1.2\,\mathrm{km}1.2km. At that point, the engines fail and the rocket is in free fall.

What height does the rocket reach in \mathrm{m}m? Assume a constant acceleration of gravity of 9.8\,\mathrm{m/s^2}9.8m/s2 even at these high altitudes.
Can anybody solve this too?

Per forum rules, please post this as a new thread AND show some attempt.

 

[Delta2]

10 The engines of a rocket sitting on the ground fire to accelerate the rocket at 3.5\,\mathrm{m/s^2}3.5m/s2 until it reaches an altitude of 1.2\,\mathrm{km}1.2km. At that point, the engines fail and the rocket is in free fall.

What height does the rocket reach in \mathrm{m}m? Assume a constant acceleration of gravity of 9.8\,\mathrm{m/s^2}9.8m/s2 even at these high altitudes.
Can anybody solve this too?

Welcome to physics forums. Here in PF we don't solve your problems for you. You have to write your attempt at the solution and we can guide you by telling you where you go wrong, giving you hints on how is the correct solution e.t.c.. As a first step post this problem as a new thread and post also your solution...