Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
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A Police Jeep is Chasing a Culprit Going on a Motorbike. the Motorbike Crosses Turning at Speed of 72 Km/H. the Jeep Follows It at a Speed of 90 Km/H, Crossing Turning Ten Seconds Later than the Bike. - Physics

Short Note

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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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:
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

\[\text{ Time }  = \frac{\text{ Distance to be covered } }{\text{ Relative velocity } } = \frac{200}{5} = 40 s\]

In 40 seconds, the police jeep moves from point A to a distance s' to catch the culprit.
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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HC Verma Class 11, 12 Concepts of Physics 1
Chapter 3 Rest and Motion: Kinematics
Q 21 | Page 52
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