Question

One stone is projected horizontally from a 20 m high cliff with an initial speed of $10m{s}^{-1}$. A second stone is simultaneously dropped from that cliff.Which of the following is true?

• A. Both strike the ground with the same velocity
• B. The ball with initial speed $10m{s}^{-1}$ reaches the ground first
• C. Both the balls hit the ground at the same time
• D. One cannot say without knowing the height of the building

Answer 1

The correct option is C Both the balls hit the ground at the same time

Initial Vertical velocity of first stone is $u_1$=0,

Initial vertical velocity of second stone is $u_2$=0,

Stone is dropped from cliff, height= $-h$=-20 m,

Let time taken by first stone to reach the ground is $t_1$ and by second stone is $t_2$.

Using $s=ut+\frac{1}{2}a{t}^2$,

$\Rightarrow -h=u{t}_1-\frac{1}{2}g{t}_1^2$ $\Rightarrow t_1=\sqrt{\frac{2h}{g}}$ ......1

$\Rightarrow -h=u{t}_2-\frac{1}{2}g{t}_2^2$ $\Rightarrow t_2=\sqrt{\frac{2h}{g}}$ ......2

Comparing equations 1 and 2, $\Rightarrow t_1=t_2$

Both the balls hit the ground at same time.