Question

An aeroplane can fly at the rate of $500\text{km/h}$ in still atmosphere (when wind is not blowing). The pilot wishes to fly through the shortest path from $A$ to $B$. The wind is blowing at the rate of $300\text{km/h}$ perpendicular to line $AB$. Find the time taken by the aeroplane to reach the point $B$ which is at a distance of $2000\text{km}$ from $A$.

• A. $10\text{hr}$
• B. $5\text{hr}$
• C. $2\text{hr}$
• D. $4\text{hr}$

Answer 1

The correct option is B $5\text{hr}$

Velocity of aeroplane w.r.t air is $500\text{km/h}$ and velocity of air is $300\text{km/h}$. As the pilot wants to reach the point $B$ through the shortest path, so he has to fly at an angle $\theta$ with $AB$, so that the resultant velocity will be in the direction of $AB$.


From the above diagram,
Resultant velocity of aeroplane is
${\overrightarrow{V}}_{\text{aeroplane}}=\sqrt{{\overrightarrow{V}}_{\text{aeroplane,air}}-{\overrightarrow{V}}_{\text{air}}^2}$
$=\sqrt{{500}^2-{300}^2}$
(since ${\overrightarrow{V}}_{air}$ is perpendicular to $AB$)
${\overrightarrow{V}}_{\text{aeroplane}}=400\text{km/h}$

Therefore, time taken by aeroplane to reach point $B$ $=\frac{2000}{400}=5\text{hr}$
So, option B is correct.