# A projectile is shot from the ground at a velocity of 15 m/s at an angle of (5pi)/12. How long will it take for the projectile to land?

Mar 31, 2017

The time is $= 2.96 s$

#### Explanation:

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

initial velocity is $u = v \sin \theta = 15 \cdot \sin \left(\frac{5}{12} \pi\right)$

distance travelled $= 0$

Acceleration is $a = - g$

We apply the equation of motion

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

$0 = 15 \sin \left(\frac{5}{12} \pi\right) \cdot t - \frac{1}{2} \cdot g \cdot {t}^{2}$

Therefore,

$t = 0$ which is the initial condition and

$t = 2 \cdot \frac{15}{g} \cdot \sin \left(\frac{5}{12} \pi\right)$

$= 2.96 s$