Question

Two bodies start falling freely from the rest from the same height at an interval of 1 s. How long after the first body begins to fall will the two bodies be 10 m apart? (g = 10 $m/s^2$)

• A. 0.5 s
• B. 1.0 s
• C. 1.5 s
• D. 2.0 s

Answer 1

The correct option is C 1.5 s

Let $x_1$ be the distance travelled by first body.

Let $x_2$ be the distance travelled by second body.

Let after $n$ seconds after fall of first body , both bodies to be 10$m$ apart.

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

$\Rightarrow -x_1=0\times n-\frac{1}{2}g{n}^2$ $\Rightarrow x_1=\frac{1}{2}g{n}^2$,

$\Rightarrow -x_2=0\times (n-1)-\frac{1}{2}g(n-1{)}^2$ $\Rightarrow x_2=\frac{1}{2}g(n-1{)}^2$,

Given $x_1-x_2=10=\frac{1}{2}g{n}^2-\frac{1}{2}g(n-1{)}^2$ $\Rightarrow n=1.5$ $s$