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Q.

A police jeep is chasing a culprit going on a motorbike. The motorbike crosses a turning at a speed of 72 kmh-1. The jeep follows it at a speed of 90 kmh-1, crossing the turning 10 s later than the bike. Assuming that they travel at constant speeds, how far from the turning will the jeep catch up with the bike? (In km)

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Detailed Solution

Vp=90kmh−1=25ms−1Vc=72kmh−1=20ms−1In 10 s culprit reaches point B from A. Distance covered by culprit,S=vt=20×10=200mAt time t = 10 s, the police jeep is 200 m behind the culprit. Relative velocity between jeep and culprit is 25 - 20 = 5 ms-1. Time =SV=2005=40s  (Relative velocity is considered) In 40 s, the police jeep will move from A to a distance S. Where S=vt=25×40=1000m=1.0 km away.The jeep will catch up with the bike 1 km far from the turning.
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