A particle is projected from the earth's surface with a velocity of...

Using equation of motion in y-dir $s = ut + \dfrac{1}{2}a{t}^{2}$

Height after $2s$,

$h = 5 = \left(\text{50 sin}\text{\theta}\right)t - \dfrac{1}{2} g {\left(t\right)}^{2}$

$5 = \left(\text{50 sin} \text{\theta}\right) \left(2\right) - \dfrac{1}{2} \cdot \text{10} \cdot {\left(2\right)}^{2}$

\dfrac{\text{25}}{\text{100}} = \text\sin \text{\theta}

\text\sin \text{\theta} = \dfrac{1}{4}

$\text{55 sin \theta} = \dfrac{55}{4} = 13 . 75$