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 (in m/s) does the bullet hits the thief’s car? 

Speed of police van $=30\times \frac{5}{18}=\frac{25}{3}m/s$

The muzzle velocity, that is velocity of bullet with respect to van

${\left[v_{bullet}\right]}_{van}={\left[v_{bullet}\right]}_{ground}-{\left[v_{van}\right]}_{ground}$

${\left[v_{bullet}\right]}_{ground}={\left[v_{bullet}\right]}_{van}+{\left[v_{van}\right]}_{ground}$

$=150+\frac{25}{3}=\frac{475}{3}m/s$

Speed of thief’s car $=192\times \frac{5}{18}=\frac{160}{3}m/s$

Now velocity of bullet with respect to the thief’s car ${\left[v_{bullet}\right]}_{car}={\left[v_{bullet}\right]}_{ground}-{\left[v_{van}\right]}_{ground}$

$=\frac{475}{3}-\frac{160}{3}=105m/s$

Hence the speed of the bullet with which it hits the thief’s car $=105m/s$