# A projectile is shot at an angle of pi/4  and a velocity of  21 m/s. How far away will the projectile land?

Mar 19, 2017

The projectile will land 45 m downfield, assuming it was launched over level ground.

#### Explanation:

Rather start from scratch (meaning the equations of motion) to solve this one, I will use an equation that can be derived for the range $R$ of a projectile:

$R = {v}_{o}^{2} / g \sin 2 \theta$

where ${v}_{o}$ is the launch speed and $\theta$ is the launch angle.

Now it is a simple matter of putting values in place of variables:

$R = {21}^{2} / 9.8 \sin \left(\frac{\pi}{2}\right) = 45 m$