Question

A 0.30 kg softball has a velocity of 15 m/s at an angle of 35 degrees below the horizontal just before making contact with the bat. What is the magnitude of the change in momentum of the ball while in contact with the bat if the ball leaves with a velocity of (a) 20 m/s, vertically downward, and (b) 20 m/s, horizontally back toward the pitcher?

Answer 1

Answer:

a) 5.03 kg m/s

b) 10.03 kg m/s

Explanation:

Hi!

Let us consider the origin of coordinates at the pitcher, and pointing directly towards the initial direction of the ball. Therefore, the angle of the velocity with respect to the x axis is -35° (below the horizontal).

The components of the initial momentum are:

px = (0.3 kg)(15 m/s) cos(-35° ) = 4.5 cos(-35° ) kg m/s = 3.69 kg m/s

py = 4.5 sin(-35° ) kg m/s = -2.581 kg m/s

The final momentum will be:

a)

pfx = 0

pfy = - (20 m/s) (0.3 kg) = -6 m/s

And the difference in momentum is:

dpy = pfy - py = -3.419 kg m/s

dpx = pfx - px = -3.69 kg m/s

And its magnitude:

dp = √(dpy^2 + dpx^2) = 5.03 kg m/s

b)

pfx = -6 kg m/s

pfy = 0

And the difference in momentum is:

dpx = pfx - px = -9.69 kg m/s

dpy = pfy - py = 2.581 kg m/s

And its magnitude:

dp = √(dpy^2 + dpx^2) = 10.03 kg m/s