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A particle is thrown with an initial spe...

A particle is thrown with an initial speed `v_(0)` at an angle `alpha` to the horizontal. Find the radius of curvature r at the highest point of its path, and its ratios to the maximum height H and to the distance L of the particle's flight.

Text Solution

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The correct Answer is:
`(r )/(H) = 2 cot^(2)alpha; (r )/(L) = (1)/(2) cot alpha`.
The speed at the uppermost point of the path is `v=v_(x)=v_(0)cos alpha`, the normal acceleration is equal to the acceleration due to gravity.
We have `r=(v^(2))/(a_(n)) = (v_(0)^(2) cos^(2)alpha)/(g)`
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