# A projectile is shot from the ground at a velocity of 24 m/s and at an angle of (2pi)/3. How long will it take for the projectile to land?

Jan 21, 2016

$4.2416 s$

#### Explanation:

Data:-
Initial velocity$= {v}_{0} = 24 \frac{m}{s}$

Angle of throwing $= \theta = \frac{2 \pi}{3}$

Time of flight=T=??

Acceleration due to gravity$= g = 9.8 \frac{m}{s} ^ 2$

Sol:-

We know that:

$T = \frac{2 {v}_{0} \sin \theta}{g}$

$\implies T = \frac{2 \cdot 24 \cdot S \in \left(\frac{2 \pi}{3}\right)}{9.8} = \frac{48 \cdot 0.866}{9.8} = 4.2416$

$\implies T = 4.2416 s$

Hence the projectile will land at $4.2416 s$ approximately.