Two identical smooth spheres collide elastically. Sphere B is initially at rest. Sphere A has velocity (10, 0) m/s. At impact, the unit vector along the line joining their centres is n = (3/5, 4/5). If the speed of sphere A after collision is N m/s, find N.
Physics · Center of maas , Momentum and Collision · collision and types of collision
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Question

Two identical smooth spheres collide elastically. Sphere B is initially at rest. Sphere A has velocity (10, 0) m/s. At impact, the unit vector along the line joining their centres is n = (3/5, 4/5). If the speed of sphere A after collision is N m/s, find N.

Physics · Center of maas , Momentum and Collision · collision and types of collision

G1 Physics · Accepted Answer

Resolve the velocity of A into normal and tangential components relative to the line of centres. Normal component magnitude: u_n = (10,0)·(3/5,4/5) = 6 m/s. Because the collision is perfectly elastic and the spheres are identical, the complete normal component is transferred from A to B. Therefore A has zero normal component after collision. The tangential component of A is unchanged because the spheres are smooth. Initial speed² = u_n² + u_t²: 10² = 6² + u_t² ⇒ u_t² = 64 ⇒ u_t = 8 m/s. Therefo…