# A soft tennis ball is dropped onto a hard floor from a height of 1.25 m and rebounds to a height of 1.05 m?

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A: Calculate its acceleration during contact with the floor if that contact lasts 3.50 ms (3.50×10-3 s) m/s.

B: How much did the ball compress during its collision with the floor, assuming the floor is absolutely rigid in m?

A: Calculate its acceleration during contact with the floor if that contact lasts 3.50 ms (3.50×10-3 s) m/s.

B: How much did the ball compress during its collision with the floor, assuming the floor is absolutely rigid in m?

##### 2 Answers

The ball accelerates at a rate of

#### Explanation:

First, we have to determine the speed the ball has at the moment it contacts the floor. Since it fell from a height of 1.25 m, the speed is found from

where

so,

(By the way, this equation of motion is commonly used when we do not know the time of the motion, and do not wish to bother with calculating it!)

Next, we find the acceleration of the ball while in contact with the floor. This time,

So, the acceleration is

Finally, to find the deformation of the ball, we do a calculation like the first one

Note that to avoid a sign conflict, I have placed a negative sign in front of the acceleration, as the ball is slowing down.

Use velocity and displacement equations for the rebound to find initial velocity. Then use this initial velocity at the time of the collision as a final velocity. Answer is:

#### Explanation:

**Question A**

After the rebound, the motion on the vertical axis is deceleration, with

Now, since it reaches 1.05 m, you have

Substituting into the height equation:

The

For educational purposes,

*This velocity will be defined as

After its collision, the ball had an acceleration from

**(Answer to question A)**

I actually have no way to answer question B. Either additional data is missing or it's a hard one. I assume it has to do with the energy difference before and after the collision and some formula for inelastic collisions. The total energy difference is measured between the two heights as dynamic difference:

Hope you find it useful.