A body is projected from the earth at an angle `30^(@)` with the horizontal with some initial velocity. If its range is 20 m, the maximum height reached by it is (in metre)

Options

A. `5 sqrt3`
B. `5/sqrt3`
C. `10/sqrt3`
D. `10/sqrt3`

Explanation

Position vector,
`vecr=hati+9hatj-3hatk`
Velocity vector,
`vecv=3hati-4hatj+5hatk`
The expression for angular momentum,L is givrn as,
`vecL=mvecr xx vecv`
implies`Ivecomega=mvecr xx vecv`
implies`mr^2vecomega=mvecr xx vevv`
`impliesvecomega=(vecr xx vecv)/|vecr|^2`
`vecr xx vecv=[[hati,hatj,hatk],[1,9,-8],[3,-4,5]]`
`=hati(45-32)-hatj(5+24)+hatk(-4_27)`
`13hati-29hatj-31hatk`
`|vecr|=|hati+9hatj-8hatk|`
`=sqrt(1^2+9^2+8^2)`
`sqrt146`
`:. vecomega=(13hati-29hatj-31hatk)/146`