could u show me how to do this physics?

Question

jim is practicing kangaroo handball, and he throws a 0.15 kg ball so that it hits a wall with a velocity of 18i + 3.2j m/s. since the wall is vertical, it changes only the ball's horizontal velocity. it exerts a force of -88.0i newtons on the ball for 0.060 secs. find the ball's intial and final momentum.

Answer 1

A force is (causes) a change in momentum with respect to time.
If you multiply the force by the length of time the force is applied, you get the net change in momentum (called an “impulse”).

The wall exerts an 88 Newton force for 0.06 seconds,
Impulse = Force * time
Impulse = 88 N * .06 s
Impulse = 5.28 Newton-seconds = 5.28 kg m/s^2 * s = 5.28 kg m/s
Change in momentum = Impulse,
Chance in momentum = 5.28 kg m/s

You know the ball’s [horizontal] initial momentum,
P = mv
P = .15 kg * 18 m/s
P = 2.7 kg m/s

You also know the ball’s change in momentum (impulse, calculated above).

So to find the final momentum, subtract the change in momentum from the initial momentum,
Final momentum = initial momentum – change in momentum
(we subtract because we called the change in momentum positive even though it is actually in the negative direction….if we originally called the change negative, we would add and not subtract),
Final momentum = 2.7 kg m/s – 5.28 kg m/s
Final momentum = -2.58 kg m/s

So the ball’s final momentum would be 2.58 kg m/s in the opposite direction.
(Meaning the ball would be traveling at 17.2 m/s in the opposite direction after the collision).

To verify this answer we can look at the problem in a different way.
A force causes an acceleration.
F = ma
While an object is acceleration, its velocity changes,
Change in velocity = acceleration * time

We know the force applied to the ball, the ball’s mass, and the time the force is applied (which is causing the acceleration), so we should easily be able to calculate the change in velocity from this and compare our answer.

F = ma
88 Newtons = .15 kg * a
a = 587 m/s^2

Change in velocity = a * t
Change in velocity = 587 m/s^2 * .06 seconds
Change in velocity = 35.2 m/s

We know our original velocity was 18 m/s in the positive direction and our change in velocity is acting in the negative direction, so our final velocity will be,
Final velocity = initial velocity – change in velocity
Final velocity = 18 m/s – 35.2 m/s
Final velocity = -17.2 m/s
Which is the same answer we previously calculated.