Question

A policeman starts giving chase 60 seconds after a stolen car zooms by at 108 km/hr. At what minimum speed should he drive if he has to catch up with the driver before he manages to get onto an expressway 60 km away?

Answer 1

Answer:

30.93 m/s

Explanation:

Given that, the speed of stolen car is,

$v_{s} =108km/hr\\v_{s} =108\times \frac{5}{18}m/s\\ v_{s} =30m/s$

As policeman start chasing the stolen car after 60 seconds.

Now suppose the speed of policeman car is, $v_{p}$

The policeman catches the stolen car at a distance of,

$S=60km\\S=60000m$

Now the distance covered by the policeman in time t is $v_{p}\times t$

And the distane cover by the thief in stolen car in time(t+60s) is $v_{s}\times (t+60sec)$.

And these distances are equal and they are equal to 60000 m.

Therefore,

$v_{p}\times t=v_{s}\times (t+60sec)=60000m$

Therfore,

$v_{s}\times (t+60sec)=60000m\\30m/s\times (t+60sec)=60000m\\(t+60s)=2000s\\t=1940s$

Now use this value to solve for minimum speed of policeman's car.

$v_{p}\times 1940=60000\\v_{p}=30.93 m/s$

Therefore minimum speed of policeman's car is 30.93 m/s.