Question

Ball $A$ having initial velocity $u=5\text{m/s}$ collides elastically with block $B$ initially at rest as shown in the figure. If both balls have the same mass, and the height of the tower is $h=20\text{m}$, find the horizontal distance $d$ traveled by ball $B$ before hitting the ground.

• A. $10\text{m}$
• B. $9\text{m}$
• C. $11\text{m}$
• D. $12\text{m}$

Answer 1

The correct option is A $10\text{m}$

As we know If masses are equal and collision is elastic, then velocities are exchanged.
$\therefore$ After collision, block $B$ will have velocity $u=5\text{m/s}$ in horizontal direction


Using equation of motion, $s_y=u_{y}t+\frac{1}{2}{a}_y{t}^2$ for motion of ball along y axis.
Given:
$s_y=-h;a_y=-g\text{and}{u}_y=0$
(as initially, ball has velocity only along x axis)
$\Rightarrow -h=0+\frac{1}{2}(-g)t^2$
$\therefore$Time of flight $t=\sqrt{\frac{2h}{g}}=\sqrt{\frac{2\times 20}{10}}=2\text{s}$
As horizontal component of velocity of ball $B=u\text{m/s}$
$\therefore d=u\times t=(5\times 2)\text{m}=10\text{m}$