Question

A helicopter is to reach a point $200000m$ east of his existing place. Its velocity relative to wind blowing at $30km{h}^{-1}$ from northwest taking scheduled arrival time duration as $40minute$ is

• A. $21\hat{i}+279\hat{j}$
• B. $279\hat{i}+21\hat{j}$
• C. $729\hat{i}+12\hat{j}$
• D. $12\hat{i}+729\hat{j}$

Answer 1

Answer: (B)

$279\hat{i}+21\hat{j}$

Velocity of wind w.r.t earth is,
$v_{WE}=30km{h}^{-1}$ towards NS. i.e SE velocity of helicopter w.r.t earth is
velocity of helicopter w.r.t. earth is $v_{HE}=\frac{200000}{1000\times (\frac{40}{60})}$ $=300km$ towards East.
In vector form,
$\overrightarrow{v_{HE}}=300\hat{i}$ and
$\overrightarrow{v_{WE}}=\left(30\cos {45}^{\circ }\right)\hat{i}-\left(30\sin {45}^{\circ }\right)\hat{j}$
$=15\sqrt{2}\hat{i}-15\sqrt{2}\hat{j}$

Then, resultant velocity is also given by , $\overrightarrow{v_{NH}}=\overrightarrow{v_{WE}}+\overrightarrow{v_{HW}}$
Velocity of helicopter w.r.t. wind is:
or $\overrightarrow{v_{HW}}=\overrightarrow{v_{HE}}-\overrightarrow{v_{WE}}$
$=300\hat{i}-(15\sqrt{2}\hat{i}-15\sqrt{2}\hat{j})$
$=279\hat{i}+21\hat{j}$