Two identical billiard balls strike a rigid wall with the same speed, and are reflected without any change of speed. The first ball strikes perpendicular to the wall. The second ball strikes the wall at an angle of 30° from the perpendicular, and bounces off at an angle of 30° from perpendicular to the wall.

(a) Determine the direction of the force on the wall due to each ball.

(b) Calculate the ratio of the magnitudes of impulses on the two balls by the wall.

Strategy for (a)

In order to determine the force on the wall, consider the force on the ball due to the wall using Newton’s second law and then apply Newton’s third law to determine the direction. Assume the -axis to be normal to the wall and to be positive in the initial direction of motion. Choose the -axis to be along the wall in the plane of the second ball’s motion. The momentum direction and the velocity direction are the same.

Strategy for (b)
Calculate the change in momentum for each ball, which is equal to the impulse imparted to the ball.