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Question

# A police van moving on a highway with a speed of 30km hâˆ’1 fires a bullet at a thief's car speeding away in the same direction with a speed of 192km hâˆ’1. If the muzzle speed of the bullet is 150msâˆ’1 , 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 105ms−1Step 1: Velocity of bullet w.r.t ground [Refer Fig.] Speeds of Cars:Police Car: V1=30×518 m/s=253 m/sThief's Car: V2=190×518 m/s=1603 m/sConcept 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=Vb−V1, 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 carVelocity of bullet w.r.t thief's carVb/2=Vb−V2 =4753−1603 m/s ∴ Vb/2=105 m/s Hence Option B is correct.

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