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

Answers (1)

\begin{aligned} &\text { Velocity of police } v_{p}=30 \mathrm{km} / \mathrm{h}=\frac{25}{3} \mathrm{m} / \mathrm{s}\\ &\text { Velocity of thief } v_{t}=190 \mathrm{km} / \mathrm{h}=\frac{160}{3} \mathrm{m} / \mathrm{s} \end{aligned}

Velocity of bullet which police is fire V_b=150 \ m/s

 

\text { final velocity of bullet muzzle from gun }=v_{b}+v_{p}=150+\frac{25}{3}=\frac{475}{3} \mathrm{m} / \mathrm{s}

Since both the vehicles are moving in the same direction, the velocity with which the bullet hits the thiefs car can be obtained as

v_{b / t}=v_{b}-v_{t}=\frac{475}{3}-\frac{160}{3}=\frac{315}{3}=105 \mathrm{m} / \mathrm{s}

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