First slide

Projectile motion

Question

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?

Moderate

A

H
B

2H
C

H/2
D

3H

Solution

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

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