Question

A ship A is moving Westwards with a speed of 10 km h^–1 and a ship B which is at 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

• 0 h

• 5 h

• `5sqrt(2)` h

• `10sqrt(2)` h

Answer 1

5 h

Explanation:

The speeds of ship A and ship B are:

`vecV_A` = 10 km/h

`vecV_B` = 10 km/h

Velocity of A w.r.t B is

`vecV_(AB) = vecV_A - vecV_B`

`|vecV_(AB)| = sqrt((10)^2 + (10)^2) = sqrt(200)`

∴ `|vecV_(AB)| = 10sqrt(2)` km/h directed along AC

Displacement, AC = `100/sqrt(2)` km

∴ Time, t = `(AC)/(|vecV_(AB)|) = (100/sqrt(2))/(10sqrt(2))`

∴ t = 5 h