Solving Momentum and Impulse: Tennis Ball Force & Velocity

[ProPM]

A tennis player is able to exert an average force of 28N when hitting a ball.

Calculate the impulse if the racket is in contact with the ball for 0.1 seconds:

Then I did: 28 x 0.1 and got 2.8 kg m/s.

The follow up question was: A 70 g tennis ball comes toward the player at 30 m/s and it hit back in the opposite direction. Show that if the contact time between the racket and ball is 0.1s, the ball leaves with a velocity of 10m/s.

So the teacher did: Change in Momentum = mv - mu

2.8 = 0.07 x 30 - 0.07 x (-10)

Ok, I tried to do it with my thinking and I got this:

The initial mv is: 30 x 0.07 = 2.1 kg m/s
The final mv is: -10 x 0.07 = -0.7

Which, equals to -2.8, which, might have been because he did initial - final momentum? Or did I do something wrong?

But anyway, the greatest problem is the fact I don't know how he knew beforehand that the change in momentum would be 2.8! I know we had to, because it asked us to SHOW. My difficulty is due to the fact that from the first question, I thought that impulse was generated when the ball was hit by the tennis player from a standstill, since a ball with a different initial velocity would have started with a lot more momentum and consequently, the change would've been much greater by the end.

I am confused, any help appreciated, thanks.

 

[mHo2]

Okay, i'll try to break this down for you using these equations

Ftotal*ΔT = ΔP
ΔP = m*ΔV

where ΔP is the change in momentum, ΔV is the change in velocity and ΔT is the change in time

Since you have a force that was applied for a certain amount of time, one would agree that this is a change in momentum, right? (much like if you slid a book across a table, the friction force would have to be acting against the book for a certain amount of time to change its velocity)

So we know that FTotal*ΔT = 2.8 kg*m/s right? Well looking at our equation up there Ftotal*ΔT = ΔP!

So that must mean that ΔP equals 2.8kg*m/s!, that means regardless of how fast that ball is going toward the player, it will experience a change in momentum of 2.8kg*m/s

so continuing with the calculation:

ΔP = m*ΔV

Since the ball goes from -30m/s to 10m/s (accounting for direction) we can say that the total change in velocity is -40m/s (V2 - V1) and the mass is 0.07kg

therefore:
2.8kg*m/s=0.07kg*40m/s
and 2.8kg*m/s = 2.8kg*m/s

The negative i believe is just because of what your teacher is considering negative and positive directions.

Hope that helped

 

[ProPM]

Definetely helped, thanks a lot mHo2.