# If a projectile is shot at a velocity of 17 m/s and an angle of pi/4, how far will the projectile travel before landing?

The projectile travels $29.45 m$
Consider the vertical equation $s \left(y\right) = v t - \frac{1}{2} a {t}^{2}$ and assume it equal to 0.
$s \left(y\right) = t \left(v - \frac{1}{2} a t\right) = 0$ so $t = 2 \frac{v}{g} = 2 v \sin \frac{45}{g} = 2.45 s$
Use this value in the horizontal equation $s \left(x\right) = v t = v \cos 45 \cdot t = v \cos 45 \cdot 2.45 = 29.45 m$