# A projectile is shot from the ground at a velocity of 2 m/s and at an angle of (pi)/2. How long will it take for the projectile to land?

Apr 11, 2018

The time is $= 0.41 s$

#### Explanation:

Resolving in the vertical direction ${\uparrow}^{+}$

The initial velocity is $u = \left(2\right) \sin \left(\frac{\pi}{2}\right) = 2 m {s}^{-} 1$

The acceleration due to gravity is $a = - g = - 9.8 m {s}^{-} 2$

Apply the equation of motion

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

$s = 0 m$

Therefore,

$0 = 2 t - \frac{1}{2} \cdot 9.8 \cdot {t}^{2}$

$4.9 {t}^{2} - 2 t = 0$

$t \left(4.9 t - 2\right) = 0$

$t = 0$ which is the initial conditions

$t = \frac{2}{4.9} = 0.41 s$