The shortest distance between the motorcyclist and the car is

10 m

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20 m

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30 m

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40 m

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Solution

The correct option is C $30 m$
Taking $N$ as $+ y - a x i s$ and E as $+ x - A x i s$
Imagine yourself as an observer siting inside the care You will regard the car as being at rest (at C) .relative to you the speed of the motorcyclist is obtained by imposing the reversed velocity of the car on motorcyclist as shown in fig $v_{m} = 15 m s^{- 1}, v_{c} = 20 m s^{- 1}$
$v_{m C} = \sqrt{15^{2} + 20^{2}} = 25, s^{- 1}$
$θ = {tan}^{- 1} (\frac{20}{15}) = 53^{o}$ with $X$ -axis
The motocyclist appears to moving the line $M P$ with speed $25^{- 1}$
The shortest distance =perpendicular distance of MP from
$C = d \to d = 50 cos 53^{o} \to d = 30 m$

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