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. 5 h
B. `5sqrt2` h
C. `10sqrt2` h
D. 0 h

Answer

A

Explanation

`vecV_A = 10 (-hati)` and `vecV_B=10 (hatj)`
`vecV_(BA)=10 hatj + 10 hati`
`=10sqrt2` km/h
Distance OB =100 cos `45^@=50sqrt2` km
Time taken to reach the shortest distance between A and B
`=(OB)/vecV_(BA) =(50sqrt2)/(10sqrt2)`=5h