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A car is moving towards south with a spe...

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.

A

`10m`

B

`20m`

C

`30m`

D

`40m`

Text Solution

Verified by Experts

The correct Answer is:
C
Taking North as + y-axis and East as `+x` Axis Imagine yourself as an observer sitting inside the car.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 figure. `v_(m)=15ms^(-1),v_(C)=20ms^(-1)`
`v_(mC)=sqrt(15^(2)+20^(2))=25ms^(-1),theta=tan^(-1)(20/15)=53^(@)`
with x-axis
The motorcyclist appears to move along the line `MP` with speed `25 ms^(-1)`.The shortest distance = perpendicular distance of `MP` from
`C = d rarr d = 50 cos 53^(@) rArr d=30m`. Time taken to come closest =time taken by motor cyclist to reach `B.t=(MB)/v_(mC)=(50sin53^(@))/25rArr t=1.6s`
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