00:01
Okay, so here we have a question about two tennis players, and we're told that tennis ball player, or player a, strikes the ball to player b with a velocity of 15 meters per second.
00:08
So it was right there and there, so 15 meters per second.
00:13
And then player b hits it back at an unknown velocity, which we need to find out.
00:19
So for part a, we are told that the average force exerted by player b's tennis racket is 130 newton's and at the time interval that the ball and the racket are in contact is 15 meters per second.
00:30
What is the impulse? so we know from the equation or force, if you will know the force, is change in momentum over time.
00:41
So force times time equals change in momentum.
00:46
And this here, force times time is what we term impulse.
00:51
So then if we just substitute our values in, so force times time is equal to, well, the force is 130.
00:58
And then we have 15 million.
01:00
Seconds so 130 multiplied by 15 times 10 to the minus three seconds and that is going to give you 1 .95 newton seconds okay and then for part b we are asked to find the velocity of the tennis ball after it leaves player b's racket so the question does tell you to pay attention to signs and this is important in this scenario so we're just going to go back to this equation here so impulse is equal to change in momentum so i'm not going to substitute in too many numbers right now just to keep it neater and cleaner so force times time is equal change momentum and change momentum is what's final momentum mv minus initial momentum m u okay and so force times time is equal to m well the m stays the same mv minus you and i'm just going to note here that the mass of the tennis ball, it must have been given in a previous part of this question, which i don't have access to, but i'm just going to go off the standard mass of a tennis ball.
02:10
So mt, the standard mass is 57 grams or 57 times 10 to the minus 3 kilograms, which is 57 grams.
02:24
So use whatever data they've given you.
02:28
However, i don't have access to that.
02:29
I'm going to use this and it'll work just fine.
02:33
So then, we want to find v.
02:35
This is the number that we want to find.
02:38
We know you, but we need to be a bit careful with the sign.
02:40
We're going to come onto that now.
02:41
So i'm going to divide through by m.
02:43
So ft over m is equal to v minus u.
02:48
Okay, then.
02:49
Now, here's when we need to pay attention.
02:51
So ft over m.
02:52
We'll deal with this left -hand sign in a bit.
02:53
So v minus.
02:55
Now, what i'm going to do is i'm going to define the, right to left hand side as being positive and the left to right hand side as being negative.
03:10
So the positive direction is right to left.
03:16
The negative direction is left to right.
03:19
This means that this velocity of minus 15 meters or 15 meters per second now becomes minus 15 meters per second because it's going in the left to right direction which i have to find as being negative.
03:31
So, v minus u, well, that u is now minus 15.
03:37
So this becomes v minus, blue back, v minus minus 15, which becomes obviously v plus 15.
03:47
Okay, so now i can substitute in our values.
03:50
So ft, we already worked out to be 1 .95...