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A boy is standinginsidea train movingwitha constant velcoity of magnitude 10m/s. He throws a ball vetically up with in speed of 5m/s relative to the train . Findthe radiusof curvature of the pathof the ball justat thetimeof projection . |
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Answer» Solution :The ball CONTINUES to movehorizontally with `(v_(x))_(0) = 10m//sec`.It begins to MOVE up with `(v_(y))= 5m//sec ` Therefore `theta_(0)` is GIVENAS `theta_(0) tan^(-1)((v_(y))/(v_(x)))` or `therefore_(0) tan^(-1) (5//10) = tan^(-1)(1//2)` Now , the required radiusofcurvature of is given as `r = (V^(2))/(g cos theta)` Putting `v = v_(0) = sqrt((v_(x))_(0)^(2) + (v_(y))_(0)^(2)),sqrt(10^(2) + 5^(2)) = 5sqrt(5)m//s` `g = 10 m//s^(2) ` and `theta = tan^(-1)(1//2)` we obtain `r~= 14 m` 
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