Question

A thief is running away on a straight road in a jeep moving with a speed of 9 m/s. A police man chases him on a motor cycle moving at a speed of 10 m/s. If the instantaneous separation of the jeep from the motorcycle is 100 m, how long will it take for the police man to catch the thief ?

Answer 1

HELLO THERE!!

We have to solve this question using the relative velocity concept.

When a person (here, the police) has to reach a destination (here, the thief) when the destination also has a velocity, we need find out the velocity of person with respect to destination.

So, here we have to find out the velocity of policeman with respect to the thief:

$v_{pt} = v_{p} - v_{t}\\=10 - 9 = 1ms^{-1}$

Now the question gets cleared!

The policeman has to cover a distance of 100m with a speed of 1 m/s to catch the thief.

From second equation of motion, we have:

$S = ut+\frac{1}{2}at^{2}\\\\\implies 100 = t +0\\or, t = 100s$

Since the policeman's motorcycle is not accelerated, we have to take a = 0, which gives t = 100s.

THANKS!