Question

A ship A is moving Westwards with a speed of 10 km $h^{-1}$ and a ship B 100 km South of A is moving northwards with a speed of 10 km $h^{-1}$. The time after which the distance between them becomes shortest is

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

Answer 1

The correct option is B $5h$

It is clear from the diagram that the shortest distance between the ship $A$ and $B$ is $PQ$.

Here, $Sin{45}^0=\frac{PQ}{OQ}$

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

Also,

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

So, the time taken to reach shortest path is

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