Question

A bus is moving with a velocity of $10m{s}^{-1}$ on a straight road. A scootorist wishes to overtake the bus in one minute. If the bus is a distance of $1.2km$ ahead, then the velocity with which he has to chase the bus is

• A. $20m{s}^{-1}$
• B. $25m{s}^{-1}$
• C. $60m{s}^{-1}$
• D. $40m{s}^{-1}$
• E. $30m{s}^{-1}$

Answer 1

Answer: (E)

$30m{s}^{-1}$

Given, velocity of bus $=10m{s}^{-1}$
Distance between bus and scootorist $=1.2km=1200m$
Let the velocity of scootorist by $v_s$
$Time=1min=60s$
Relative velocity of scootorist w.r.t. bus
$=(v_2-10)m{s}^{-1}$
We know that, $time=\frac{velocity}{relativevelocity}$
$\Rightarrow 60=\frac{1200}{v_s-10}$
$\Rightarrow 60(v_s-10)=1200$
$\Rightarrow 60v_s-600=1200$
$\Rightarrow 60v_s=1200+600$
$\Rightarrow 60v_2=1800$
Velocity of a scootorist,
$\therefore v_s=\frac{1800}{60}=30m{s}^{-1}$.