Question

A thief is running away on a straight road in a jeep moving with a speed of $9{\text{ms}}^{-1}$. A policeman chases him on a motor cycle moving at a speed of $10{\text{ms}}^{-1}$. If the instantaneous separation of the jeep from the motor cycle is $100\text{m}$, how long will it take for the policeman to catch the thief?

• A. $1\text{s}$
• B. $19\text{s}$
• C. $90\text{s}$
• D. $100\text{s}$

Answer 1

The correct option is D $100\text{s}$

We have,
$v_p=10m/s$ - Speed of policeman
$v_t=9m/s$ - Speed of thief

Relative speed of policeman with respect to thief :
$v_{pt}=v_p-v_t=10-9=1m/s$

As the distance between policeman and thief is $100m$, the time required for policeman to reach the thief is:
$t=\frac{100}{v_{pt}}=\frac{100}{1}=100s$