# A projectile is shot from the ground at a velocity of 23 m/s at an angle of pi/3. How long will it take for the projectile to land?

Oct 22, 2016

The time is $3.98$s

#### Explanation:

We use the formula

y = y_0 + v_0yt + ½at^2

${v}_{0} = 23 \sin \left(\frac{\pi}{3}\right)$

$y = {y}_{0} = 0$

$a = - g$
We need to find t

$0 = 0 + 23 t \sin \left(\frac{\pi}{3}\right) - \frac{g {t}^{2}}{2}$

So $t = 0$ or $t = \frac{2 \cdot 23 \sin \left(\frac{\pi}{3}\right)}{g}$

Take $g = 10$

Then $t = \frac{2 \cdot 23 \sin \left(\frac{\pi}{3}\right)}{10} = \frac{23 \sin \left(\frac{\pi}{3}\right)}{5} = 3.98 s$