A smooth sphere was moving on a smooth horizontal surface at a speed of when it collided with a smooth vertical wall. The motion direction of the sphere at the instant of collision formed an angle of with the wall. Its speed immediately after the collision was . Determine the coefficient of restitution between the sphere and the wall.
A smooth snooker ball is moving at a speed of 7.9 m/s on a smooth snooker table. It strikes one of the smooth cushions of the table at an angle of . Given that the coefficient of restitution between the ball and the cushion is , find the ball’s speed and the angle its path makes with the cushion after the impact, rounding the answer to one decimal point.
A smooth sphere of mass 2 kg sliding along a horizontal plane collided with a stationary smooth sphere of mass 5 kg. Just before the collision, the first sphere was moving at 6 m/s and its direction of motion made an angle of with the line of centers of the spheres. Given that the coefficient of restitution between the spheres is , find the velocity of the first sphere after the collision. Express the magnitude of this velocity in meters per second and the direction of the velocity as the angle made with the line of centers of the spheres. Give both values correct to one decimal place.