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A car is moving towards south with a speed of 20m/s. A motor cyclist is moving towards east with a speed of 15m/s. At a certain instant, the mortcyclist is due south of the car and is at a distance of 50m form the car. Find the shortest distance between the motorcyclist and the car. Also find the time after which they are closest to each other.
Dear Prateek,
let t be the time from the instant when the bike is due south. distance squared = (50-20t)2 +(15t)2= 625t2-2000t +2500
='s'. ds/dt=0, 1250t-2000=0, tmin=1.6 seconds, d2s/dt2=1250t=1250*1.6>0, minimum distance=√s at t=1.6 =√900=30m
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