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  4. 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?

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Q. 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?

Motion in a Plane

Solution:

image
$A C=R / 2, P C=H$
We have to find $h=M P$.
From the previous solution, we know that if $H=R$, then
$\tan \theta=4$
Now $\tan \theta=\frac{M C}{A C}=\frac{M P+P C}{A C}$
$4 =\frac{h+H}{R / 2} \Rightarrow 4=\frac{(h+H) 2}{H}$
$\Rightarrow h =H$