# A sphere A, of mass 3 kg, is moving on a smooth horizontal floor with speed 4 m/s in a direction which is at right-angles to a smooth vertical wall. The sphere strikes the wall and rebounds with a...

A sphere A, of mass 3 kg, is moving on a smooth horizontal floor with speed 4 m/s in a direction which is at right-angles to a smooth vertical wall. The sphere strikes the wall and rebounds with a speed of 2.8 m/s.

After *A *has rebounded from the wall, it catches up and collides directly with another sphere* B, *of mass 5 kg, which is travelling with speed 1.5 m/s in the same direction as *A. *The coefficient of restitution between spheres *A *and *B *is 0.6. Calculate the speed of *A* and the speed of *B *after the collision.

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### 2 Answers

The sphere A, of mass 3 kg moving on a smooth horizontal floor with speed 4 m/s in a direction at right-angles to a smooth vertical wall, strikes the wall and rebounds with a speed of 2.8 m/s. It later catches up and collides directly with sphereB of mass 5 kg, which is traveling with speed 1.5 m/s in the same direction as A*. *The coefficient of restitution between spheres *A *and *B *is 0.6.

If the initial and final velocity of A is `U_A` and `V_A` and the initial and final velocity of B is `U_B` and `V_B` , the coefficient of restitution relates them as: 0.6 = `(V_B - V_A)/(U_B - U_A)`

`U_B - U_A` = 1.3 m/s

`V_B - V_A` = 1.3*0.6 = 0.78

It is not possible to determine the actual velocity of A and B after collision with the information provided. Only the relative velocity of the two can be determined and it is 0.78 m/s

The question is

After *A *has rebounded from the wall, it catches up and collides directly with another sphere*B, *of mass 5 kg, which is travelling with speed 1·5 ms–1 in the same direction as *A. *Thecoefficient of restitution between spheres *A *and *B *is 0·6. Calculate the speed of *A*and thespeed of *B *after the collision.