Question

Inspector Ram Singh on a police jeep is chasing a culprit, going on a motorcycle. The motorcycle crosses a turning at a speed of $72km/h$. The jeep follows it at a speed of $90km/h$, crossing the turning 10 seconds later than the motorcycle. Assuming they travel at constant speeds, how far(in km) from the turning will Ram Singh catch up with the culprit?

Answer 1

$\text{Speed of motorcycle while crossing turning = 72 km/h= 20 m/s}$
$\text{Speed of jeep while crossing turning = 90 km/h= 25 m/s}$
Jeep crosses the turn 10 s later than the motorcycle
$\therefore$ Separation between culprit and police when police jeep is going to cross the turning$=20\times 10=200\text{m}$
Let after time $t$ both police and culprit meet,
then, $S_{\text{police}}=S_{\text{culprit}}+200$
$\Rightarrow 25t=20t+200$
$\Rightarrow 5t=200$
$\therefore t=40\text{s}$
$\therefore$ Distance covered by police to catch the culprit = $25\times 40=1000\text{m=1 km}$