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Question: A police van moving on a highway with a speed of 30 km h<sup>-1</sup> fires a bullet at a thief’s ca...

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 km h-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

Answer

105 m s-1

Explanation

Solution

Speed of police van w.r.t. ground VPG=30kmh−1V_{PG} = 30kmh^{- 1}Speed of thief’s Car w.r.t. groundVTG=192kmh−1V_{TG} = 192kmh^{- 1}Speed of bullet w.r.t. police van

VBP=150ms−1=150×185kmh−1=540kmh−1V_{BP} = 150ms^{- 1} = 150 \times \frac{18}{5}kmh^{- 1} = 540kmh^{- 1}

Speed with which the bullet will hit the thier’s car will be

VBT=VBG+VGT=VBP+VPG+VGT=540kmh−1+30kmh−1−192kmh−1V_{BT} = V_{BG} + V_{GT} = V_{BP} + V_{PG} + V_{GT} = 540kmh^{- 1} + 30kmh^{- 1} - 192kmh^{- 1}

(∵VGT=−VTG\because V_{GT} = - V_{TG})

378kmh−1=378×518ms−1378kmh^{- 1} = 378 \times \frac{5}{18}ms^{- 1}

=105ms−1= 105ms^{- 1}