A billiard ball is moving in the x-direction at 33.4 cm/s and strikes another billiard ball moving in the y-direction at 38.9 cm/s.As a result of the collision,the first ball moves at 50.6 cm/s,and the second ball stops.In what final direction does the first ball move?
A)in the x-direction
B)at an angle of 49.4° ccw from the x-direction
C)at an angle of 40.6° ccw from the x-direction
D)at an angle of 56.6° ccw from the x-direction
E)Such a collision cannot happen.

Question

Quizplus · Accepted Answer

The direction of the first ball after the collision can be found using vector addition and trigonometry. Since the second ball stops, all its momentum is transferred to the first ball. The angle θ with the x-axis can be found using tan(θ) = opposite/adjacent = velocity in y-direction / velocity in x-direction. Given the final velocities, tan(θ) = 38.9 / 33.4. Solving for θ gives an angle of 49.4°, indicating the ball moves at an angle of 49.4° counterclockwise from the x-direction.

A Billiard Ball Is Moving in the X-Direction at 33