# A projectile is shot from the ground at a velocity of 84 m/s and at an angle of (7pi)/12. How long will it take for the projectile to land?

Aug 5, 2017

$t = 16.5$ $\text{s}$

#### Explanation:

We're asked to find the time it takes for a projectile to land, given its initial velocity.

To do this, we can use the kinematics equation

ul(Deltay = v_0sinalpha_0t - 1/2g t^2

where

• $\Delta y$ is the change in height (which is $0$ when it lands)

• ${v}_{0}$ is the initial speed (given as $84$ $\text{m/s}$)

• ${\alpha}_{0}$ is the launch angle (given as $\frac{7 \pi}{12}$)

• $t$ is the time (what we're trying to find)

• $g = 9.81 \textcolor{w h i t e}{l} {\text{m/s}}^{2}$

Plugging in known values, we have

$0 = \left(84 \textcolor{w h i t e}{l} {\text{m/s")sin((7pi)/12)t - 1/2(9.81color(white)(l)"m/s}}^{2}\right) {t}^{2}$

$\left(4.905 \textcolor{w h i t e}{l} \text{m/s"^2)t^2 = (81.1color(white)(l)"m/s}\right) t$

(4.905color(white)(l)"m/s"^2)t = 81.1color(white)(l)"m/s"

t = color(red)(ulbar(|stackrel(" ")(" "16.5color(white)(l)"s"" ")|)