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Question

A police van moving on a highway with a speed of 30km h1 fires a bullet at a thief's car speeding away in the same direction with a speed of 192km h1. If the muzzle speed of the bullet is 150ms1 , with what relative speed does the bullet hit the thief's car?

A
95ms1
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B
105ms1
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C
115ms1
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D
125ms1
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Solution

The correct option is B 105ms1

Step 1: Velocity of bullet w.r.t ground [Refer Fig.]
Speeds of Cars:
Police Car: V1=30×518 m/s=253 m/s

Thief's Car: V2=190×518 m/s=1603 m/s

Concept of Muzzle Speed:
Muzzle speed is the speed of bullet with respect to the gun, just after firing.
Here the speed of gun is same as that of Police car and bullet is fired in the same direction as the car.
Vmuzzle=Vb/1
Vmuzzle=VbV1, Where Vb is the Velocity of bullet w.r.t ground

Vb=Vmuzzle+V1

=150 m/s +253 m/s

=4753 m/s
Step 2: Velocity of bullet w.r.t. thief's car
Velocity of bullet w.r.t thief's car
Vb/2=VbV2

=47531603 m/s
Vb/2=105 m/s
Hence Option B is correct.

2111416_936918_ans_c5d982d9996b480cb1d39d821ea32454.png

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