A police van moving on a highway with a speed of 30 km h-1 fires a bullet at a thief’s car speeding away in the same direction with a speed of 192 km h-1 . If the muzzle speed of the bullet is 150 m s-1 , with what speed does the bullet hit the thief’s car ?

Question

A police van moving on a highway with a speed of 30 km h-1 fires a bullet at a thief’s car speeding away in the same direction with a speed of 192 km h-1 . If the muzzle speed of the bullet is 150 m s-1 , with what speed does the bullet hit the thief’s car ? (A)  95 m s-1  (B)  105 m s-1  (C)  115 m s-1  (D)  125 m s-1

Tardigrade Admin · Accepted Answer

Speed of police van w.r.t. ground ∴ vPG=30 km h-1 Speed of thiefâs car w.r.t. ground ∴ vTG=192 km h-1 Speed of bullet w.r.t. police van vBP=150 ms-1=150×(18/5)km h-1=540 km h-1 Speed with which the bullet will hit the thiefâs car will be vBT=vBG+vGT=vBP+vPG+vGT =540 km h-1+30 km h-1-192 km h-1 (∵ vGT=-vTG) =378 km h-1=378×(5/18) ms-1=105 ms-1

Q. A police van moving on a highway with a speed of $30 km h^{- 1}$ fires a bullet at a thief’s car speeding away in the same direction with a speed of $192 km h^{- 1}$ . If the muzzle speed of the bullet is $150 m s^{- 1}$ , with what speed does the bullet hit the thief’s car ?

$95 m s^{- 1}$

$105 m s^{- 1}$

$115 m s^{- 1}$

$125 m s^{- 1}$

Q. A police van moving on a highway with a speed of 30kmh−1 fires a bullet at a thief’s car speeding away in the same direction with a speed of 192kmh−1 . If the muzzle speed of the bullet is 150ms−1 , with what speed does the bullet hit the thief’s car ?

95ms−1

105ms−1

115ms−1

125ms−1

Q. A police van moving on a highway with a speed of $30 km h^{- 1}$ fires a bullet at a thief’s car speeding away in the same direction with a speed of $192 km h^{- 1}$ . If the muzzle speed of the bullet is $150 m s^{- 1}$ , with what speed does the bullet hit the thief’s car ?

$95 m s^{- 1}$

$105 m s^{- 1}$

$115 m s^{- 1}$

$125 m s^{- 1}$