Question

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

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

Answer 1

The correct option is D $5h$

$\overrightarrow{V_A}=-10\hat{i}$
$\overrightarrow{V_B}=10\hat{j}$
$\overrightarrow{V_{B/A}}=\overrightarrow{V_B}-\overrightarrow{V_A}$
$\overrightarrow{V_{B/A}}=10\hat{j}+10\hat{i}=10\sqrt{2}\left(\frac{\hat{i}+\hat{j}}{\sqrt{2}}\right)$
The shortest distance is ac, which will be at time when B reaches point c from b,
$t=\frac{bc}{V_{B/A}}=\frac{\frac{100}{\sqrt{2}}}{10\sqrt{2}}=5h$