Question

A police jeep is chasing with velocity of 45 km/h, a thief in another jeep moving with velocity 153 km/h. Police fire a bullet with muzzle velocity of 180 m/s. The velocity it will strike the car of thief is:
A.) 150 m/s
B.) 27 m/s
C.) 450 m/s
D.) 250 m/s

Answer 1

Hint: We will first convert the given units of velocity in SI units. Then, the effective velocity or the relative velocity will come into picture and we will find the effective velocity of the bullet while leaving the police vehicle by adding the velocities. Then, we will find out the velocity with which the bullet hits the thief’s jeep by subtracting its velocity from the effective velocity of the bullet.

Complete step by step solution
We have been given the velocity of the police jeep ${v}_{p}=45\; km/h=\dfrac{5}{18}\times 45\; m/s=12.5\; m/s$

And the velocity of thief’s jeep ${v}_{t}=153\; km/h=\dfrac{5}{18}\times 153\; m/s=42.5\; m/s$

And the velocity of bullet ${v}_{b}=180\; m/s$

According to the question, the bullet has been fired from the jeep of the police, and both the police and the jeep will be moving in the same direction as the bullet. So, the effective velocity of bullet while leaving the police jeep will be ${v}_{1}={v}_{p}+{v}_{b}=12.5+180=192.5$ m/s.

Now, the velocity with which the bullet will strike the jeep of the thief $={v}_{1}-{v}_{t}=192.5-42.5=150$ m/s.

Hence, option a is the correct answer.

Note: The important concept that has been used here is the effective velocity, in which the direction plays an important role. The velocities were added, when the bullet left the police jeep while it was subtracted when it hit the thief’s jeep and this is the point where many can make mistakes while solving.