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. ` 0 h, ` 100 km`
B. ` 5 h, 50 sqrt 2 km`
C. ` 5 sqrt 2 h, 50 km`
D. ` 10 sqrt 2 h, ` 50 sqrt km`

Answer

B

Explanation

Let the ships ` A` and ` B` be at positions shown in Fig. 2 (CF). 54, when the distance betance between them is shortest.
Relative velocity of ` B w.r.t. A` is
` v_1 = sqrt (v-1^2+ v_^2^2) = sqrt (10^2 + 10^2)`
` = 10 sqrt 2 km//h` along ` BC`.
.
The shortest distance between ` A` and `C` is (d) given by ` , d= AC= AB sin 45^@`
` = 100 xx 1/(sqrt 2) = 50 sqrt 2 km`
Shortest time ` t= d/v_2= (50 sqrt 2)/(10 sqrt 2) = 5 h`.