Question

A police jeep is chasing with velocity 45 km/h a thief in another jeep moving with velocity 153 km/h. Police fire a bullet with muzzle velocity of 180m/s. The velocity it will strike the car of the thief is-

A. 150m/s
B. 27 m/s
C. 450 m/s
D. 250 m/s

Answer 1

Hint: Calculate the relative velocity with respect to the ground reference system as the speed of the thief’s jeep is in the ground reference system.

Complete step by step answer:
Let us look at the following diagram:

It is given that the velocity of the police jeep is 45 km/h.
First, let us convert it to m/s as the options are in this unit.
$45km/h=45\times \dfrac{1000}{3600}m/s$
$=45\times \dfrac{5}{18}m/s$
$=12.5m/s$
The muzzle velocity of the bullet is 180m/s. As the muzzle of the gun is also moving at a velocity of 12.5 m/s, a ground observer will see the velocity of the bullet to be,
Observed bullet velocity = Muzzle velocity of the bullet + Muzzle’s velocity (Velocity of the police jeep).
$=(180+12.5)=192.5$m/s
Hence, the bullet velocity with respect to a ground observer is =192.5m/s
Now, let us convert the velocity of the thief’s jeep into m/s,
$153km/h=153\times \dfrac{5}{18}m/s$
$=42.5m/s$

Hence the relative velocity of the bullet with respect to the thief’s jeep is given by,

Relative velocity = (Velocity of bullet - Velocity of the thief’s jeep).

Both these velocities are taken with respect to a ground observer.

So, the bullet will hit the thief’s jeep at a speed of,
$=(192.5-42.5)=150$m/s

Hence, the correct option is (A).

Note: You should always fix a ground observer and solve the question in that perspective. It reduces the chance of making a mistake while calculating relative velocity and actual velocity of an object. Relative velocity is an important concept while solving the questions of inelastic or elastic collision. So, choosing an observer is a vital segment for this kind of problem.