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Question

A motorbike is being chased by a car. The motorbike moves with the speed of 10 m/s and has acceleration of 5 m/s2. Whereas, the car has speed of 20 m/s and accelerates with 3 m/s2. If the initial separation between motorbike and car is 60 m, find the distance by which car will miss the motorbike.

A
25 m
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B
30 m
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C
35 m
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D
40 m
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Solution

The correct option is C 35 m
Let vm and vc be the speed of motorbike and car respectively, am and ac be the acceleration of motorbike and car respectively and Scm be the distance covered by the car w.r.t motorbike.
So, from relative frame (considering only car is moving)
Speed of car w.r.t motorbike is,vcm=vcvm=2010=10 m/s
And, acceleration of the car w.r.t motorbike is,acm=acam=35=2 m/s2
Since the car is retarding, it will stop in some time ( w.r.t bike )
So, from equation of motion we have
v2=v2cm+2acmScm
0=1022×2×Scm
Scm=25 m
Since, the initial separation between car and motorbike is 60 m and distance chased by the car is 25 m
Thus, the distance by which car has missed the motorbike is 6025=35 m

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