# A projectile is shot from the ground at a velocity of 19 m/s at an angle of pi/4. How long will it take for the projectile to land?

Jan 14, 2017

The time is $= 2.74 s$

#### Explanation:

Vertical motion ${\uparrow}^{+}$

$u = 19 \sin \left(\frac{\pi}{4}\right) m {s}^{-} 1$

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

$y = u t + \frac{1}{2} a {t}^{2}$

$0 = 19 \sin \left(\frac{\pi}{4}\right) t - \frac{1}{2} \cdot 9.8 \cdot {t}^{2}$

$t = 0$ or $t = 19 \sin \frac{\frac{\pi}{4}}{4.9} = 2.74 s$

Horizontal motion ${\rightarrow}^{+}$

$u = 19 \cos \left(\frac{\pi}{4}\right) m {s}^{-} 2$

$x = 2.74 \cdot 19 \cdot \cos \left(\frac{\pi}{4}\right) = 36.84 m$