Question

One body is dropped, while a second body is thrown downward with an initial velocity of $1{\text{ms}}^{-1}$ simultaneously. After what time separation between the two bodies is $18\text{m}$?

• A. $4.5\text{s}$
• B. $9\text{s}$
• C. $18\text{s}$
• D. $36\text{s}$

Answer 1

The correct option is C $18\text{s}$

Let $t$ be the time after which the separation between two bodies is $18\text{m}$
Let $S_{rel}$ be the relative distance between two bodies after time $t$
$\Rightarrow S_{rel}=18\text{m}$
Relative acceleration of two bodies during downfall $=a_{rel}=g-g=0$
Relative initial velocity of two bodies $u_{rel}=1-0=1\text{m/s}$
$S_{rel}=u_{rel}t+\frac{1}{2}{a}_{rel}{t}^2$
$\Rightarrow 18=1\times t+0$
$\Rightarrow t=18\text{s}$