First slide

Relative motion based problems

Question

A policeman moving on a highway with a speed of 30 km $h^{- 1}$ fires a bullet at 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?

Moderate

A

120 m $s^{- 1}$
B

90 m $s^{- 1}$
C

125 m $s^{- 1}$
D

105 m $s^{- 1}$

Solution

Velocity of police van = $30 \times \frac{5}{18} = \frac{25}{3} m s^{- 1}$ ,Muzzle speed of the bullet = 150 m $s^{- 1}$
Speed of the bullet w.r.t. ground = [150 + (25/3)] m $s^{- 1}$
Velocity of thief's car is $192 \times \frac{5}{18} = \frac{32 \times 5}{3} = \frac{160}{3} m s^{- 1}$
Relative velocity of bullet w.r.t. thief's car is $150 + \frac{25}{3} - \frac{160}{3} = 150 - \frac{135}{3} = 105 m s^{- 1}$

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