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

30.93 m/s

Step-by-step explanation:

Given that, the speed of stolen car is,

`v_(s) =108km/hr\\v_(s) =108* (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)* t`

And the distane cover by the thief in stolen car in time(t+60s) is
`v_(s)* (t+60sec)`.

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

Therefore,

`v_(p)* t=v_(s)* (t+60sec)=60000m`

Therfore,

`v_(s)* (t+60sec)=60000m\\30m/s* (t+60sec)=60000m\\(t+60s)=2000s\\t=1940s`

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

`v_(p)* 1940=60000\\v_(p)=30.93 m/s`

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