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Q.
A body is projected with an angle $\theta$. The maximum height reached is $h$. If the time of flight is $4s$ and $g$ is $10\, m/s^2$, then value of $h$ is
Motion in a Plane
Solution:
The projectile is shown below
$t =\frac{2 u \sin \theta}{ g }$
$\Rightarrow 4=\frac{2 u \sin \theta}{ g }$
Also, $v^{2}=u^{2}+2$ as
$\Rightarrow 0^{2}=u^{2} \sin ^{2} \theta-2 g h$
$\frac{u^{2} \sin ^{2} \theta}{2 g}=h$
From equation (ii)
$\frac{ u ^{2} \sin \theta}{ g }=2$
$\Rightarrow \frac{4 g ^{2}}{2 g }= h$
$h =2\, g$
$h =20\, m$
