A car is moving towards south with a speed of `20 m s^(-1)`. A motorcyclist is moving towards east with a speed of `15 s^(-1)`. At a certain instant, the motorcyclist is 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. a. `1//3 s`
B. b. 8/3 s`
C. `1//5 s`
D. `8//5 s`

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`,
.