Question

A helicopter is flying horizontally at $8\text{m/s}$ at an altitude $180\text{m}$ when a package of emergency medical supplies is ejected horizontally backward with a speed of $12\text{m/s}$ relative to the helicopter. Ignoring air resistance what is the horizontal distance(in $m$) between the package and the helicopter when the package hits the ground ?

Answer 1

Relative velocity of package wrt helicopter $\overrightarrow{V_{ph}}=\overrightarrow{V_{pg}}-\overrightarrow{V_{hg}}$
$-12\hat{i}=\overrightarrow{V_{pg}}-8\hat{i}$
${\overrightarrow{V}}_{pg}=-12\hat{i}+8\hat{i}=-4\hat{i}$
Using second equation of motion
Time taken by package to hit the ground $180=\frac{1}{2}\times 10t^2\Rightarrow t=6\text{sec}$
distance between package and helicopter $=|\overrightarrow{V_{pg}}|t+|\overrightarrow{V_{hg}}|t$
$=4\times 6+8\times 6$
$=72\text{m}$