Automatic A if You Answer This Question

[Fizzix]

"Automatic A if You Answer This Question"

My astronomy proffessor gave us this question in class today, and said anybody that could answer it would receive an automatic A. You would think that'd it be really hard but it doesn't look too dificult.

There is a block with mass "M" which is at a height "H" above a ball with mass "m." (M>>m) In an elastic collision where the block is dropped straight down onto the ball, at what height "h" will the ball bounce?

No quantities given.

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/........./ M
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l
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H
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.....m......

 

[cristo]

Well, I'm hardly going to answer a question that'll give you an A in a class am I?

 

[ogb p]

I would approach this question by first identifying the known and unknown quantities. From the given information, we know that there is a block with mass "M" at a height "H" above a ball with mass "m." We also know that the collision between the block and the ball is elastic, meaning that kinetic energy is conserved. The unknown quantity is the height "h" at which the ball will bounce.

Next, I would use the laws of conservation of energy and momentum to solve for the unknown quantity. Since the collision is elastic, we know that the total kinetic energy before the collision is equal to the total kinetic energy after the collision. Using the equation for kinetic energy (KE = 1/2 * mass * velocity^2), we can set up an equation with the known masses and velocities before and after the collision.

We also know that momentum is conserved in an elastic collision. This means that the total momentum before the collision is equal to the total momentum after the collision. Using the equation for momentum (p = mass * velocity), we can set up another equation with the known masses and velocities before and after the collision.

By solving these two equations simultaneously, we can find the velocity of the ball after the collision. Then, using the equation for kinetic energy, we can solve for the height "h" at which the ball will bounce.

In conclusion, while this question may seem difficult at first glance, with the application of conservation laws and basic physics equations, we can determine the height at which the ball will bounce and receive an automatic A.