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Biker

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## Homework Statement

A tennis ball has a mass of 75 g that is placed above a basketball has a mass of 590 g. Both are stationary and They were dropped from a height about 1.2 m ( The collisions are perfectly elastic)

1) Calculate the speed of the basketball when it reaches the ground

2) Calculate the height that the tennis ball will reach

## Homework Equations

P = m v

F t = m dv

## The Attempt at a Solution

Okay, so part one is pretty easy

1) sqrt(2 g 1.2) = 4.89 m/s (Use g as 10)

Now for the 2nd part, It is common that the ratio is 3 ( The speed of the tennis ball is 3 multiplied by the initial speed of it)

However I didnt get that through my calculations ( 2.55)

Here is my solution:

V1: Speed of the basketball

V2: Speed of the tennis ball

1 = v2 -v1/u1 - u2

u1-u2 = v2 -v1

(Without needing to extract this equation through kinetic energy and momentum)

Now the basketball will rebound with the same speed (assuming it is instantaneous) but moving upward

And it will now have a collision with the tennis ball that is moving downward with the same speed

So

4.89--4.89 = v2 - v1

9.79 = v2 - v1

v1 = v2 - 9.79

Now Substitute that in the momentum equation

M* 4.89 - m * 4.89 = M * (v2 - 9.79) + 0.075 v2

Place the value of M and m

and V2 ( Velocity of the tennis ball) will equal to 12.48 m/s.

For the ratio, 12.48/4.89 = 2.55

http://hyperphysics.phy-astr.gsu.edu/hbase/doubal.html

Here is the site for a reference about the ratio.

I assume that the mistake might be in that they assume if the top ball hits the bottom one, the bottom one's velocity doesn't change which is a mistake.

And according to my calculations, A ratio of 3 will only result if the m of the tennis ball is 0 which can't happen... Weird

There are various of ways to solve this question, and all of them yield in the same result

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