Question

A boy standing at a corner noticed a thief on bike moving with $54km/h$. After some time, a police jeep crosses him with speed $72km/h$. If the jeep catches the thief at a distance of $1km$ from the boy, then the time gap (in $s$) between the bike and the jeep, when they cross the boy, is

Answer 1

Given,
Velocity of thief bike $=54km/h$
$=54\times \frac{5}{18}=15m/s$
Velocity of police jeep $=72km/h$
$=72\times \frac{5}{18}=20m/s$
Let the police jeep catches the thief in time $t$, then
$1000=20t$
$t=50s$
$1000=15(t+\Delta t)$
$1000=15(50+\Delta t)$
$1000=750+15\Delta t$
$250=15\Delta t$
$\Delta t=\frac{50}{3}=16.67s$