Question

A billiard ball of mass m = 0.25 kg strikes the cushion of a billiard table at θ₁ = 62° and a speed v₁ = 28 m/s. It bounces off at an angle of θ₂ = 43⁰ and a velocity of v₂ = 11 m/s. What is the magnitude of its change in momentum (in kg·m/s)?

Answer 1

here,

mass of billard ball, m = 0.25 kg
velocity, vi = 28 m/s
final velocity, vf = 11 m/s

Intial momentum
horizontal moementum, Pix = m*vi*Cos62 = 0.25 *28 * Cos62 = 3.286 kg.m/s
vertical moementum, Piy = m*vi*Sin62 = 0.25 *28 * Sin62 = 6.181 kg.m/s

Final momentum
horizontal moementum, Pfx = m*vf*Cos43 = 0.25 *11 * Cos43 = 2.011 kg.m/s
vertical moementum, Pfy = m*vf*Sin43 = 0.25 *11 * Sin43 = 1.875 kg.m/s

net change of momentum in horizontal direction :
Px = 2.011 - 3.286 = - 1.275 Kg.m/s

net change of momentum in vertical direction :
Px = - 6.181 + 1.875 = - 4.306 kg.m/s

Net magnitude, |p| = sqrt( 1.275^2 + 4.306^2 )
Net magnitude, |p| = 4.491 kg.m/s