# A projectile is shot from the ground at a velocity of 1 m/s and at an angle of (5pi)/6. How long will it take for the projectile to land?

Jan 3, 2016

$T = 0.10204 s$

#### Explanation:

Data:-
Velocity$= V = 1 \frac{m}{s}$
Angle$= \theta = \frac{5 \pi}{6}$
Time of flight =T=??
Sol:-
Time of flight is given by$= \frac{2 {V}_{0 y}}{g}$
where ${V}_{0 y}$ is the y-component of velocity and $g$ is acceleration due to gravity whose value is (9.8 m/s^2).

Y-component of velocity$= {V}_{0 y} = V \sin \theta = 1 \cdot \sin \left(\frac{5 \pi}{6}\right) = 0.5$

$T = \frac{2 {V}_{0 y}}{g} = \frac{2 \cdot 0.5}{9.8} = \frac{1}{9.8} = 0.1020 s$

$\implies T = 0.10204 s$