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

Options

A. 0
B. 5 h
C. `5sqrt2h`
D. `10sqrt2h`

Answer

B

Explanation

(b):
`vecu_(AB)+vecu_(A)=vecu_(B)`
`vecu_(BA)=vecu_(B)-vecu_(A)`
`u_(BA)=sqrt(u_(A^(2))+v_(B^(2)))`
`u_(BA)=sqrt(10^(2)+10^(2))=10sqrt2m`
For shortest distance OM, ship B has to travel BO
`BO=100 cos 45^(@)`
`=(100)/(sqrt2)km`
`70.71 km`
Time taken to reach the shortest path between M and B
`t=(BO)/(|v_(BA)|)=((100)/(sqrt2))/(10sqrt2)`
`t=5` hours