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Two smooth identical balls A and B, each of mass m and radius R, are placed in a plane. The centre of A is at (0, R) and the centre of B is at (5R, -R). Ball A moves along the positive x-direction with speed 4 m/s and strikes the stationary ball B. The collision is perfectly elastic. Determine the speed of ball A immediately after the collision and the magnitude of the impulse that A exerts on B (take m = 1 kg).

1. Speed of A = 2*sqrt(3) m/s; Impulse = 2m N*s
2. Speed of A = 2 m/s; Impulse = 4m N*s
3. Speed of A = sqrt(3) m/s; Impulse = m N*s
4. Speed of A = 4 m/s; Impulse = 0

Correct answer: Speed of A = 2*sqrt(3) m/s; Impulse = 2m N*s

Solution

The line of centres makes an angle with the x-axis; A's velocity along this line transfers entirely to B (equal masses, elastic), leaving A with only the tangential component, giving speed 2*sqrt(3) m/s and impulse 2m N*s.

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