Coefficient of Restitution problem

[CCC1212]

Hello, I have this simple COR problem that I seem to be a bit stuck on.

Homework Statement

A 1.25 kg squash racquet swung at 37 m/s contacts a ball moving at 42 m/s in the opposite direction. Immediately after impact the racquet has a velocity of 25 m/s and the ball has a velocity of 50 m/s. What is the coefficient of restitution associated with the impact?

Homework Equations

I've been using e= (V1-V2)/(U1-U2)

The Attempt at a Solution

When I use this equation I get 5, but obviously that's wrong since it shouldn't be greater than 1.

Can anyone point me in the right direction? Thanks so much

 

[PeroK]

Can anyone point me in the right direction? Thanks so much

The operative word is direction!

 

[CCC1212]

The operative word is direction!

I sort of had a feeling this may be the case. Should I be using "U1+U2" instead of "U2-U1". Or am I way off?

 

[PeroK]

I sort of had a feeling this may be the case. Should I be using "U1+U2" instead of "U2-U1". Or am I way off?

Then depends on the direction of $U_1$ and $U_2$. Are you using speeds or velocities?

 

[CCC1212]

Then depends on the direction of $U_1$ and $U_2$. Are you using speeds or velocities?

Velocities since it says 'in the opposite direction' I'm assuming.

 

[PeroK]

Velocities since it says 'in the opposite direction' I'm assuming.

So, what are the initial velocities of the racket and ball?

 

[CCC1212]

They are 37 m/s (racket) and 42 m/s (ball)

Ahhh I think I see what you may be getting at. Because it says the ball is moving in the opposite direction, should I be writing the equation like...

50-25/37- -42

 

[PeroK]

They are 37 m/s (racket) and 42 m/s (ball)

No, for velocities that can't be correct if they are in opposite directions.

Ahhh I think I see what you may be getting at. Because it says the ball is moving in the opposite direction, should I be writing the equation like...

50-25/37- -42

Only if you know why!

 

[CCC1212]

No, for velocities that can't be correct if they are in opposite directions.

Could you explain that statement. I thought the difference between speed and velocity is that velocity considers direction?

 

[PeroK]

Could you explain that statement. I thought the difference between speed and velocity is that velocity considers direction?

When you have a problem in 1D it's up to you to decide what direction is positive and what direction is negative. In this case I might decide that the racket is moving in the positive direction, which means that the velocity of the racket is $37m/s$.

The ball is moving in the opposite direction, so its velocity must be $-42 m/s$.

 

[CCC1212]

When you have a problem in 1D it's up to you to decide what direction is positive and what direction is negative. In this case I might decide that the racket is moving in the positive direction, which means that the velocity of the racket is $37m/s$.

The ball is moving in the opposite direction, so its velocity must be $-42 m/s$.

Ahhh of course. Thanks so much!