Question

A ball moving with velocity $\stackrel{\wedge }{i}$ collides with a stationary wall and returns with a velocity $\stackrel{\wedge }{j}/2$. The coefficient of restitution for this collision is :

• A. $1/2$
• B. $1/3$
• C. $1/4$
• D. $1/5$

Answer 1

The correct option is C $1/4$

From the figure,

The velocity of approach, $v_1=\left(1\right)cos\theta$

The velocity of separation, $v_2=\frac{1}{2}sin\theta$

The coefficient of restitution, $e=\frac{v_2}{v_1}$

$e=\frac{1}{2}\frac{sin\theta }{cos\theta }$

$e=\frac{1}{2}tan\theta$. . . . .(1)

From triangular figure,

$tan\theta =\frac{1}{2}$

Now, equation (1) becomes,

$e=\frac{1}{4}$

The correct option is C.