Question

A police jeep on patrol duty on a national highway was moving with a speed of 54km/h. In the same direction, they found a thief rushing up in a car at a rate of 126km/h. Police sub-inspector fired at the car of the thief with his service revolver with a muzzle speed of 100m/s. With what speed will the bullet hit the car of the thief?

Answer 1

Hint: Remember that the total speed of the bullet fired would be the sum of the speeds of the police jeep and the muzzle speed of the service revolver used by the policeman. Now you could recall the expression for relative velocity. Then you could find the relative velocity of the bullet with respect to the thief’s car and this would be the speed to be found.

Formula used:
Relative velocity of A with respect to B,
${{V}_{AB}}={{V}_{A}}-{{V}_{B}}$

Complete Step by step solution:
In the question we have a police jeep moving at 54km/h and a thief moving at a speed of 126km/h in a car in the same direction. The police sub-inspector fires at the car with a muzzle speed of 100m/s. We are asked to find the speed at which the bullet hit the car of the thief.

Speed of the police jeep
${{v}_{j}}=54km/h=54\times \dfrac{5}{18}m/s=15m/s$

Muzzle speed of the revolver,
${{v}_{m}}=100m/s$

Total velocity of the bullet = speed of the car + muzzle speed of revolver
${{V}_{b}}={{v}_{j}}+{{v}_{m}}$

Velocity of the thief’s car,
${{v}_{t}}=126km/h=126\times \dfrac{5}{18}m/s=35m/s$

The relative velocity of the bullet with respect to the thief would be the difference in velocity of the bullet with the velocity of the thief’s car. That is,
${{V}_{bt}}={{V}_{b}}-{{v}_{{{t}_{{}}}}}$
$\Rightarrow {{V}_{bt}}=115-35$
$\therefore {{V}_{bt}}=80m{{s}^{-1}}$
This will be the velocity at which the bullet will hit the thief’s car.

Hence, we found the velocity at which the bullet will hit the thief’s car to be 80m/s.

Note:
While solving numerical problems like this, one should make sure that all the given quantities are in their SI unit or at least in the same unit. Otherwise, necessary conversion should be done. Now, for a quantity given in km/h we could convert into m/s by recalling,
$1km/h=1\times \dfrac{1000}{3600}m/s=\dfrac{5}{18}m/s$
This is how we have converted the given quantities in the question.