Question

A particle of mass m strikes on ground with a velocity v at an angle of incidence 45° . If the coefficient of restitution; e = 1/√2 ; the velocity of reflection and the angle of reflection are

(1) √3/2 v ; tan^-1 (1/√2)

(2) v ; 45°

(3) v/√2 ; 45°

(4) √3/2 v ; tan^-1√2

Answer 1

(4) √3/2 v ; tan^-1√2

Let v’ and θ denote the velocity after reflection and the agnle of reflection as shown in Fig.

Before reflection v_x = v cos 45° = v/√2 and v_y = v sin 45° = v/√2

As there is no force along horizontal; v_x = v_x = v/√2

The surface exerts a force along the vertical.