# A projectile is shot from the ground at a velocity of 5 m/s at an angle of (5pi)/12. How long will it take for the projectile to land?

Jan 30, 2017

The answer is $0.99 s$

#### Explanation:

Resolving in the vertical direction ${\uparrow}^{+}$

$u = 5 \sin \left(\frac{5}{12} \pi\right) m {s}^{-} 1$

$a = - g m {s}^{-} 2$

$s = 0 m$

We use the equation

$s = u t + \frac{1}{2} a {t}^{2}$

$0 = 5 \sin \left(\frac{5}{12} \pi\right) \cdot t - \frac{g}{2} {t}^{2}$

$t \left(5 \sin \left(\frac{5}{12} \pi\right) - \frac{g}{2} t\right) = 0$

Therefore,

$t = 0$, this is when the projectile is shot

and

$5 \sin \left(\frac{5}{12} \pi\right) - \frac{g}{2} t = 0$

$t = \frac{10}{g} \sin \left(\frac{5}{12} \pi\right)$

$t = \frac{10}{9.8} \sin \left(\frac{5}{12} \pi\right) = 0.99 s$