Question

A piece of marble is projected from the earth's surface with a velocity of $50m{s}^{-1}$ . 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 ___ ( $g=10m{s}^{-2}$ )

Answer 1

Answer: 4

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