A projectile is shot from the ground at a velocity of 86 m/s at an angle of pi/3. How long will it take for the projectile to land?

Oct 21, 2016

Time = 14.5 s

Explanation:

We use the vertical direction to determine the time in the air.

$y = {y}_{0} + {v}_{0 y} t + \frac{1}{2} {a}_{y} {t}^{2}$

In this case
$y = 0$
${y}_{0} = 0$
${v}_{0 y} = 82 \sin \left(\frac{\pi}{3}\right)$
${a}_{y} = - g$
So we have
$0 = 0 + 82 t \sin \left(\frac{\pi}{3}\right) - \frac{1}{2} g {t}^{2}$
So $t = 0$
or $t = \frac{2 \cdot 82 \cdot \sin \left(\frac{\pi}{3}\right)}{g} = \frac{2 \cdot 82 \cdot \sqrt{3}}{2 \cdot 9.8} = 14.5 s$