Question

A police jeep is chasing a culprit going on a motorbike. The motorbike crosses a turning at a speed of 72 km/h, The jeep follows it at a speed of 90 km/h, crossing the turning ten seconds later than the bike. Assuming that they travel at constant speeds, how for from the turning will the jeep catch up with the bike?

Answer 1

Step 1, Given data

Velocity of the police jeep $V_p$ = 90km/h = 25 m\s

Velocity of the culprit $V_e$ = 72km/h = 20 m\s

Step 2, Finding the distance

In 10 sec culprit travels some distance

Distance covered by culprit,

S = vt = $20\times 10=200m$

At time t = 10 sec, the police jeep is 200 m behind the Culprit.

Relative velocity between police jeep and culprit,

Velocity of jeep - Velocity of culprit

Or,

25-20 = 5 m/s

Time = $\frac{s}{v}$ = $\frac{200}{5}$ = 40 s (Relative velocity is considered).

Is 40 s, the plolice jeep will move from A to a distance S,

Where, S = vt =$25\times 40$ = 1000 m = 1.0 km away.

$\therefore$ The jeep will catch up with the bike, 1 km far from the turning.