Billiard ball A of mass mA = 0.115 kg moving with speed vA = 2.80 m/s strikes ball B , initially at rest, of mass mB = 0.144 kg . As a result of the collision, ball A is deflected off at an angle of θ′A = 30.0∘ with a speed v′A = 2.10 m/s , and ball B moves with a speed v′B at an angle of θ′B to original direction of motion of ball A.

Part A

Taking the x axis to be the original direction of motion of ball A , choose the correct equation expressing the conservation of momentum for the components in the x direction.

Taking the x axis to be the original direction of motion of ball A, choose the correct equation expressing the conservation of momentum for the components in the x direction.

0=mAv′Asinθ′A−mBv′Bsinθ′B
mAvA=mAv′Acosθ′A+mBv′Bcosθ′B
mAvA=mAv′Acosθ′A−mBv′Bsinθ′B
0=(mAvA+mBv′B)sinθ′B

Part B

Taking the x axis to be the original direction of motion of ball A , choose the correct equation expressing the conservation of momentum for the components in the y direction.

mAvA=mAv′Acosθ′A−mBv′Bsinθ′B
0=(mAvA+mBv′B)sinθ′B
0=mAv′Asinθ′A−mBv′Bsinθ′B
mAvA=mAv′Acosθ′A+mBv′Bcosθ′B

Part C

Solve these equations for the angle, θ′B , of ball B after the collision. Do not assume the collision is elastic.

Part D

Solve these equations for the speed, v′B , of ball B after the collision. Do not assume the collision is elastic.