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A particle of mass m is projected with v...

A particle of mass m is projected with velocity v at an angle `theta` with the horizontal. Find its angular momentum about the point of projection when it is at the highest point of its trajectory.

Text Solution

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At the highest point it has only horizontal velocity
`v_(x) = v cos theta`
Length of the perpendicular to the horizontal velocity from .O. is the maximum height, where
`H_(max) = (v^(2) sin^(2) theta)/(2g)`
The required angular momentum,
`L = (mv^(3) sin^(2) theta cos theta)/(2g)`, which is directed along negative z-axis.
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