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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.
```

6 years ago

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```
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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6 years ago

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