9) Two identical billiard balls are traveling in opposite directions: ball A is

Question

9) Two identical billiard balls are traveling in opposite directions: ball A is traveling east at 2.0 m/s, while ball B is traveling west at 1.0 m/s. The balls collide at a glancing angle so that ball B is traveling north after the collision with a velocity of 1.3 m/s. What is the velocity (magnitude and direction) of ball A after the collision? 9) Two identical billiard balls are traveling in opposite directions: ball A is traveling east at 2.0 m/s, while ball B is traveling west at 1.0 m/s. The balls collide at a glancing angle so that ball B is traveling north after the collision with a velocity of 1.3 m/s. What is the velocity (magnitude and direction) of ball A after the collision?

Explanation / Answer

Let the ball A has velocity Vx and Vy in x and y - direction respectively

conserving the momentum in x - direction we have

m*2 + m*-1 = m*Vx + m*0

Vx = 1 m/s

conserving the momentum in y- direction we have

m* 0 + m*0 = m*Vy + m*1.3

Vy = -1.3 m/s

so magnitude of velocity of ball A = sqrt(1^2+ 1.3^2) = 1.64 m/s

directoion = tan^-1(1.3 / 1) =52.43 o south of east

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