# If a projectile is shot at an angle of pi/4 and at a velocity of 12 m/s, when will it reach its maximum height??

Jan 15, 2017

The maximum height is $= 3.67 m$

#### Explanation:

The vertical motion is ${\uparrow}^{+}$

$u = 12 \sin \left(\frac{\pi}{4}\right) m {s}^{-} 1$

$v = 0 m {s}^{-} 1$

$a = - g = - 9.8 m {s}^{-} 2$

We use the equation

${v}^{2} = {u}^{2} + 2 a s$

$0 = 144 {\sin}^{2} \left(\frac{\pi}{4}\right) - 2 \cdot 9.8 \cdot h$

$h = \frac{144 \cdot {\sin}^{2} \left(\frac{\pi}{4}\right)}{2 \cdot 9.8} = 3.67 m$