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# Answer this simple physics question

 07-07-2013, 11:28 PM #1 Unaffiliated Registered User     Join Date: Aug 2010 Location: Richmond, B.C. Country: Posts: 10,116 vCash: 50 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.
 07-08-2013, 12:25 AM #2 Dave º     Join Date: Oct 2009 Posts: 3,444 vCash: 500 70m/s?
07-08-2013, 12:37 AM
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 Originally Posted by Dave 70m/s?
Agreed?

 07-08-2013, 01:09 AM #4 Zaide I'm a renegade     Join Date: Aug 2009 Location: Quebec City Country: Posts: 64,456 vCash: 50 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. __________________ Last edited by Zaide: 07-08-2013 at 01:58 AM.
07-08-2013, 02:29 AM
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 Originally Posted by Zaide 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)

 07-08-2013, 06:45 AM #6 Dave º     Join Date: Oct 2009 Posts: 3,444 vCash: 500 Would've got it anyway, coefficient of restitution.
07-08-2013, 10:21 AM
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 Originally Posted by Unaffiliated Neglect friction, drag...

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 07-08-2013, 10:42 AM #8 Richer's Ghost Moderator awww summertime     Join Date: Apr 2007 Location: photoshop labor camp Country: Posts: 47,519 vCash: 425 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. Last edited by Richer's Ghost: 07-08-2013 at 10:56 AM.
 07-08-2013, 04:49 PM #9 Beef Invictus Global Moderator Wing or Retire!     Join Date: Dec 2009 Location: Alexandria Country: Posts: 36,312 vCash: 156 We need to prove this experimentally. __________________ Down in the basement, I've got a Craftsman lathe. Show it to the children when they misbehave.
 07-09-2013, 11:24 AM #10 Razor29 52-22-8     Join Date: Sep 2011 Country: Posts: 7,094 vCash: 50 I volunteer someone that is not me to do this.
 07-09-2013, 01:04 PM #11 Anglesmith Moderator Fancyman of Cornwood     Join Date: Sep 2012 Location: Victoria Country: Posts: 7,073 vCash: 400 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.
 07-16-2013, 10:36 AM #12 EmeticDonut Registered User     Join Date: Oct 2006 Posts: 3,432 vCash: 50 I think you should try doing your homework by yourself.
07-16-2013, 01:45 PM
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 Originally Posted by EmeticDonut I think you should try doing your homework by yourself.

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