A ship A is moving Westwards with a speed of `10kmh^(-1)` and a ship B 100km South of A is moving northwards with a speed of `10kmh^(-1)`. The time after which the distance between them shortest is

Options

A. `0h`
B. `5h`
C. `5sqrt(2)h`
D. `10sqrt(2)h`

Answer

b

Explanation

It is clear from the digram that the shortest distance between the ship A and B is PQ

Here, sin `45^(@)=(PQ)/(OQ)implies100xx(1)/(sqrt(2))=50sqrt(2)m`
Also `v_(AB)=sqrt(v_(A)^(2)+v_(B)^(2))=sqrt(10^(2)+10^(2))=10sqrt(20km//h`
So, time taken for them to reach shortest path is
`t=(PQ)/(v_(AB))=(50sqrt(2))/(10sqrt(2))=5h