# A projectile is shot from the ground at a velocity of 1 m/s at an angle of pi/4. How long will it take for the projectile to land?

Jan 17, 2017

The time is $= 0.144 s$

#### Explanation:

Computing in the vertical direction

${\uparrow}^{+}$

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

$y = 0$

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

We use the equation

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

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

$t \left(\sin \left(\frac{\pi}{4}\right) - 4.9 t\right) = 0$

Therefore,

$t = 0$ which is the initial time

$t = \frac{1}{4.9} \sin \left(\frac{\pi}{4}\right) = 0.144 s$