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# A particle is projected from ground at some angle with the horizontal. let P be the point At maximum height H. At what height above the point P should the particle be aimed to have range equal to maximum height

Khimraj
3007 Points
3 years ago
max height = range
u2sin$\Theta$/2g  = 2u2sin$\Theta$cos$\Theta$/g
½ = 2cos$\Theta$
then
cos$\Theta$ = ¼
then
tan$\Theta$ = $\sqrt{15}$
let height above point is x then
tan$\Theta$  = (H+x)/(H/2) = $\sqrt{15}$
then x = (H/2)($\sqrt{15}$ – 2)
Hope it clears.