Question

A police jeep on a petrol duty on a national highway was moving at a speed of 54 km/hr. In the same direction. It found that a thief was rushing in a car moving at a speed of 126 km/hr. The police sub-inspector fired at the car of the thief with his service revolver with a muzzle speed of 100 m/s. with what speed will the bullet hit the car of a thief?

Answer 1

Step 1: Given data

$$\begin{gathered} Speedofpolicejeep=54km{h}^{-1} \\ Muzzlespeed=speedofbulltew.r.tpolicjeep=100m{s}^{-1} \end{gathered}$$

$velocityoftheif=126km/h$

Step 2: Calculating the speed

$$\begin{gathered} Speedofpolicejeep=speedofgun=54km{h}^{-1}=15m{s}^{-1} \\ Muzzlespeed=speedofbulltew.r.tpolicjeep=100m{s}^{-1} \end{gathered}$$

Now we'll calculate the total velocity of the bullet.

$Totalvelocityofbullet=Speedofthecar+muzzlespeed=115m{s}^{-1}(100+15)$

$velocityoftheif=126km/h=35m/s$

The relative velocity of bullet w.r.t. thief $=Totalvelocityofthebullet–Velocityofthethief’scar=115-35=80m/s$

Therefore the bullet will hit the car of the thief at 80 m/s.

Hence, with the speed of 80 m/s, the bullet hit the car of a thief.