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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.

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.

Grade:12

1 Answers

Chetan Mandayam Nayakar
312 Points
10 years ago

 

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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Chetan Mandayam Nayakar – IIT Madras

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