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 far from the turning will the jeep catch up with the bike?
Solution
Velocity of the police jeep, vp = 90 km/h = 25 m/s
Velocity of the culprit riding the motorbike, vc = 72 km/h = 20 m/s
In 10 seconds, the culprit reaches point B from point A.
Distance covered by the culprit:
s = vct = 20 × 10 = 200 m
At time t = 10 s, the police jeep is 200 m behind the culprit.
Relative velocity between the police jeep and the culprit:
25 − 20 = 5 m/s
In 40 seconds, the police jeep moves from point A to a distance s' to catch the culprit.
Here,
s' = vpt = 25 × 40
⇒ s' = 1000 m = 1.0 km
Thus, the jeep will catch up with the bike 1.0 km away from the turning.
