Consider an elastic collision in two dimensions. A 0.5-kg ball at rest, located at the origin, is struck by another ball (of equal mass) moving in the +x direction. After the collision, one of the balls is moving with a velocity of 2 m/s at an angle of 30º above the +x axis. The y momentum of the other ball is:
A) -1.0 y kgm/s. .
B) +0.5 y kgm/s. .
C) +1.0 y kgm/s. .
D) -0.5 y kgm/s. .

Question

Quizplus · Accepted Answer

Since the collision is elastic and involves balls of equal mass, momentum is conserved in both the x and y directions. The ball moving at 2 m/s at a 30º angle above the +x axis has a y-component of velocity given by $v_y = 2 \sin(30^\circ) = 1 \, \text{m/s}$. The momentum in the y direction for this ball is $p_y = mv_y = 0.5 \times 1 = 0.5 \, \text{kgm/s}$. Since the total y momentum before the collision was 0 (as both balls were moving along or at rest on the x-axis), the y momentum of the other ball must be equal in magnitude but opposite in direction to conserve momentum, hence -0.5 kgm/s.

Consider an Elastic Collision in Two Dimensions