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 hr
B. 5 hr
C. `5sqrt2 hr `
D. `10 sqrt2 hr`

Answer

B

Explanation

`|vecV _(AB)| = sqrt ( 10 ^(2) + 10 ^(2)) = 10 sqrt2 kmph`
distance `OB = 100 cos 45 ^(@) = 50 sqrt2km`
Time taken to reach the shortest distance between
`A&B = (50 sqrt2)/( |vecV _(BA)|) = (50 sqrt2)/(10 sqrt2)`
`t _(sn) = 5 hrs.`