Question

A ship $A$ is moving Westwards with a speed of $10$ km/h and a ship $B$ $100$ km South of $A$, is moving Northwards with a speed of $10$ km/h. The time after which the distance between them becomes shortest, is?

• A. $5$ h
• B. $5\sqrt{2}$ h
• C. $10\sqrt{2}$ h
• D. $0$

Answer 1

The correct option is A $5$ h

$sin{45}^{\circ }=\frac{PQ}{OQ}$

$PQ=100\times \frac{1}{\sqrt{2}}=50\sqrt{2}m$

$also{V}_{AB}=\sqrt{V_A^2+V_B^2}=\sqrt{{10}^2+{10}^2}=10\sqrt{2}km/h$

time taken of r to reach the shortest part

$t=\frac{PQ}{V_{AB}}=\frac{50\sqrt{2}}{10\sqrt{2}}=5h$