A thief is running away on a straight road on a jeep moving with a speed of $9\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$. A police man chases him on a motor cycle moving at a speed of $10\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$. If the instantaneous separation of jeep from the motor cycle is $100m$, how long will it take for the policemen to catch the thief ?

The correct option is D

$100sec$

Step 1. Given Data:

Speed of thief jeep $v_j=9\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$

Speed of police motorcycle $v_m=10\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$

Distance between motorcycle and jeep $s=100m$

Let the relative velocity of the policeman with respect to the thief be $v_p$.

Step 2. The relative velocity $v_p$ of the policeman with respect to the thief is:

$$\begin{gathered} v_p=v_m-v_j \\ v=10–9 \\ v=1\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right. \end{gathered}$$.

Step 3. The time is taken by the policeman to catch the thief:

We know that,

Speed $=$Distance$/$time

$$\begin{gathered} v=\frac{s}{t} \\ t=\frac{s}{v} \\ t=\frac{100}{1} \\ t=100sec \end{gathered}$$

Hence, the correct option is (D).