Speed, Impulse of Billiards Physics

Question

Hi,

During a game of billiards, the 145g cue ball, travelling at 10.4m/s, glances off of a stationary 164g billiard ball so that the billiard ball moves off at 35m/s, at an angle of 35 degrees from the cue ball's original path. Find the following:

a. New speed of the cue ball

b. Impulse imparted by the cue ball on billiard ball

Answer 1

a)

P0 = P'

Px0 = Px', Py0 = Py' (Momentum is conserved in both directions, x and y, and movement in both directions are independent)

X-direction:

m(cue) * v0x(cue) + m(bil) * v0x(bil) = m(cue) * v'x(cue) + m(bil) * v'x(bil)

0.145 kg * 10.4 m/s + (0) = 0.145 kg * v'x(cue) + 0.164 kg * 35 m/s * cos(35˚)

v'x(cue) = -22.027 m/s

Y-direction:

m(cue) * v0y(cue) + m(bil) * v0y(bil) = m(cue) * v'y(cue) + m(bil) * v'y(bil)

(0) + (0) = 0.145 kg * v'y(cue) + 0.164 kg * -35 m/s * sin(35˚)

v'y(cue) = 22.706 m/s

v'(cue) = √(v'x(cue)^2 + v'y(cue)^2)

v'(cue) = 23.186 m/s

b) Impulse = P' - P0

Impulse = m(bil) * v'(bil) - m(bil) * v0(bil)

Impulse = 0.164 kg * 35 m/s - (0) = 5.74 kg m/s