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Answer this simple physics question

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Old
07-07-2013, 11:28 PM
  #1
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Answer this simple physics question

A train is travelling towards you at 30 m/s. You throw a tennis ball at it at 10 m/s, and it bounces off the train head-on in a perfect elastic collision. Neglect friction, drag, etc.

What is the final speed of the tennis ball (relative to the ground)?



Hint: The answer is not 40 m/s.

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07-08-2013, 12:25 AM
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70m/s?

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07-08-2013, 12:37 AM
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Quote:
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70m/s?
Agreed?

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Old
07-08-2013, 01:09 AM
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Zaide
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What are the mass

But yeah, I think 70 m/s is correct.

The ball will bounce back, relative to the train, with a velocity of 40 m/s. Since the train is going at 30 m/s relative to the ground, then the ball is going at 70 m/s relative to the ground.

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07-08-2013, 02:29 AM
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Quote:
Originally Posted by Zaide View Post
What are the mass

But yeah, I think 70 m/s is correct.

The ball will bounce back, relative to the train, with a velocity of 40 m/s. Since the train is going at 30 m/s relative to the ground, then the ball is going at 70 m/s relative to the ground.


I described it to myself as:
In the train's reference frame, the ball is approaching the stationary train at 40 m/s. Since it is a perfect elastic collision, the ball rebounds off the train, now moving at 40 m/s in the opposite direction.

A coordinate translation back to the initial reference frame of the thrower yields 40 m/s + 30 m/s = 70 m/s.





Maybe I shouldn't have given that hint. Or would you guys have got it anyway?

Also, do you think we should post these kinds of questions every once in a while to this forum? (questions that don't really require much math, but have somewhat unexpected answers)

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07-08-2013, 06:45 AM
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Would've got it anyway, coefficient of restitution.

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07-08-2013, 10:21 AM
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Neglect friction, drag...

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07-08-2013, 10:42 AM
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plot twist: the train is being driven by Neo from the matrix.

there is no ball.

Kidding aside I would have failed and said 40.


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Old
07-08-2013, 04:49 PM
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We need to prove this experimentally.

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07-09-2013, 11:24 AM
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I volunteer someone that is not me to do this.

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07-09-2013, 01:04 PM
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Consider the train as the frame of reference, initially not moving, and the tennis ball travelling toward it at 40mph. In a perfect elastic collision, we need to conserve both momentum and kinetic energy. That means that if the speed of the ball is s and the speed of the train is S, and the mass of each is m and M respectively, and we denote final speeds by s' an S',

s'm + S'M = -40m
S' = -(40m-s'm)/M

If we assume that the ball's mass is negligible compared to the train, then this is very close to zero, and the train is propelled imperceptibly slowly in the negative direction. In order to preserve kinetic energy, then the ball has the same speed with respect to the train as it did before, 40mph.

Then the answer is that the ball's final velocity relative to the ground is 70mph.

EDIT: Just realized the answer was already provided above.

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Old
07-16-2013, 10:36 AM
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I think you should try doing your homework by yourself.

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Old
07-16-2013, 01:45 PM
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Quote:
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I think you should try doing your homework by yourself.
Reading comprehension failure.

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