A car is moving towards south with a speed of `20 m s^(-1)`. A motorcycst is moving towards east with a speed of `15 m s^(-1)`. At a crttain instant, the motorcyclistis due south of the car and is at a distance of `50 m`from the car.
The shortest distance between the motorcyclist and the car is.

Options

A. `20 m`
B. `10 m`
C. `40 m`
D. `30 m`

Answer

d

Explanation

`CM =50 m`
`v_(1) =20 m s^(-1)`, V_(2) =15 m s^(-1)`,
`AC=v_(1) t, MB=v_(2)t`
` S=sqrt(MA^(2)+MB^(2))=sqrt((50-v_(1)t)^(2)+(v_(2))t^(2))`
From `(ds)/(dt) =0` (for minima), find `t` and put `t` in `s`,
.