# A projectile is shot from the ground at a velocity of 7 m/s and at an angle of (7pi)/12. How long will it take for the projectile to land?

Oct 3, 2016

Let the velocity of projection of the projectile be u with angle of projection $\alpha$ with the horizontal direction.
The vertical component of the velocity of projection is $u \sin \alpha$ and the horizontal component is $u \cos \alpha$

Now if the time of flight be T then the object will return to the ground after T sec and during this T sec its total vertical displacement h will be zero. So applying the equation of motion under gravity we can write
$h = u \sin \alpha \times T + \frac{1}{2} g {T}^{2}$

$\implies 0 = u \times T - \frac{1}{2} \times g \times {T}^{2}$

$\text{where "g = "acceleration due to gravity}$

$\therefore T = \frac{2 u \sin \alpha}{g}$

In the given problem

$u = 7 \text{m/s" and alpha=(7pi)/12 " } g = 9.8 \frac{m}{s} ^ 2$

$T = \frac{2 \times 7 \times \sin \left(\frac{7 \pi}{12}\right)}{9.8} = 1.38 s$