A thief in a stolen car passes through a police check post at his top speed of `90 kmh^-1.` A motorcycle cop, reacting after 2 s, accelerates from rest at `5 ms^-2.` His top speed being `108 kmh^-1.` Find the maximum separation between policemen and thief.

Options

A. `112.5 m`
B. `115 m`
C. `116.5 m`
D. None of these

Answer

A

Explanation

`90 km//h=90xx5/18=25 m//s`
`180 km//h=108xx5/18=30 m//s`
At maximum separation their velocities are same.
`:.` Velocity of motorcycle=`25 m//s`
or `at=25`
or `t=5s`
But thief has travelled up to 7s.
`s_1` =displacement of thief
`=v_1 t_1=25xx7=175m`
`s_2`=displacement of motorcycle
`=1/2xxa_2t_2^2`
`=1/2xx5xx(5)^2`
`=62.5m`
`:.` Maximum separation
`=s_1-s_2=112.5 m`