A police van moving on a highway with a speed of $30 ext{ km/h}$ fires a bullet at a thief's car sp

Question

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

Professor PC Thomas Classes · Answer

Speed of police van $v_p = 30	ext{ km/h} = 30 	imes \frac{5}{18} = \frac{25}{3}	ext{ m/s}$. Muzzle speed $v_m = 150	ext{ m/s}$. Speed of bullet with respect to ground $v_b = v_p + v_m = \frac{25}{3} + 150 = \frac{475}{3}	ext{ m/s}$. Speed of thief's car $v_t = 192	ext{ km/h} = 192 	imes \frac{5}{18} = \frac{160}{3}	ext{ m/s}$. Speed of bullet relative to thief's car $= v_b - v_t = \frac{475}{3} - \frac{160}{3} = \frac{315}{3} = 105	ext{ m/s}$.