First slide
Relative velocity in 1-d
Question

A police jeep is chasing a culprit going on a motorbike. The motorbike crosses a turning at a speed of 72 km h-1. The jeep follows it at a speed of 90 km h-1, crossing the turning 10 s later than the bike. The distance (in km) from turning point at  which the police catch the culprit is ________ .

Moderate
Solution

vp=90kmh1=25ms1,vc=72kmh1=20ms1
In 10 s  culprit reaches point B from A. 

Distance covered by culprit,s=vt=20×10=200m.
At time t = 10 s, the police jeep is 200 m behind the culprit. Relative velocity between jeep and culprit is 2520=5ms1
Time =sv=2005=40s
In 40 s, the police jeep will move from A to a distance s where, s=vt=25×40=1000m=1.0km away. The jeep will catch the bike 1 km far from the turning point. 

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