Question

A piece of marble is projected from the earth's surface with a velocity of $50ms^{- 1}$ . Two seconds later, it just clears a wall $5m$ high. The angle of projection is $\theta $ . Then the value of $\frac{1}{sin \theta }$ is ___ ( $g=10ms^{- 2}$ )

Answer 1

Using the equation of motion in $y$ -direction $s=ut+\frac{1}{2}at^{2}$
Height after $2s$ ,
$h=5=\left(50 sin \theta \right)t-\frac{1}{2}g\left(t\right)^{2}$
$5=\left(50 sin \theta \right)\left(2\right)-\frac{1}{2}\cdot 10\cdot \left(2\right)^{2}$
$\frac{25}{100}=sin\theta $
$\text{sin}\theta =\frac{1}{4}$
$\theta=\sin ^{-1}\left(\frac{1}{4}\right)$