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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 far from the turning will the jeep catch up with the bike?
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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.
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