A bus is moving with a velocity of 10 `ms^(-1)` on a straight road. A scootorist wishes to overtake the bus in one minute. If the bus is at a distance of 1.2 km ahead, then the velocity with which he has to chase the bus is

Options

A. `20 ms^(-1)`
B. `30 ms^(-1)`
C. `60 ms^(-1)`
D. `40 ms^(-1)`

Answer

B

Explanation

Given, velocity of bus = 10 m`s^(-1)`
Distance between bus and scootorist = 12 km
= 1200 m
Let the velocity of scootorist be `v_(s)`
Time = 1 min = 60 s
Relative velocity of scootorist w.r.t. bus
`=(v_(s)-10)ms^(-1)`
We know that, `"time"=("distance")/("relative velocity")`
`rArr60=1200/(v_(s)-10)`
`rArr60(v_(s)-10)=1200`
`rArr60v_(s)-600=1200`
`rArr60v_(s)=1200+600`
`rArr60v_(s)=1800`
Velocity of a scootorist,
`thereforev_(s)=1800/(60)=30ms^(-1)`