Question

A ball with a speed of 9 m/s collides with another identical ball at rest. After the collision, the direction of each ball makes an angle of 30° with the original direction. The ratio of velocities of the balls after collision is x : y, where x is _________

Hint:

In symmetric collisions where identical particles scatter at equal angles, their final speeds must be equal to conserve momentum in the transverse direction.

Answer 1

Correct Answer: 1

Step 1: In an oblique collision of identical masses where both move at the same angle $\theta$ to the original path, the situation is symmetrical.
Step 2: Conservation of momentum perpendicular to the original direction: $m v_1 \sin 30^\circ - m v_2 \sin 30^\circ = 0$.
Step 3: This directly implies $v_1 = v_2$.
Step 4: Therefore, the ratio $v_1 : v_2$ is $1 : 1$. Thus, $x = 1$.