# A projectile is shot from the ground at a velocity of 4 m/s at an angle of (5pi)/12. How long will it take for the projectile to land?

Feb 9, 2016

${x}_{\max} \cong 0 , 408 \text{ m}$

#### Explanation:

$\theta = \frac{5 \cancel{\pi}}{12} \cdot \frac{180}{\cancel{\pi}}$
$\theta = {75}^{o}$
$g = 9 , 82 \frac{m}{s} ^ 2$
$\sin 2 \theta = {150}^{o} = \sin {30}^{o} = 0 , 5$
${x}_{\max} = \frac{{v}_{i}^{2} \cdot \sin 2 \theta}{2 \cdot g}$
${x}_{\max} = \frac{{4}^{2} \cdot 0 , 5}{2 \cdot 9 , 81}$
${x}_{\max} = \frac{16 \cdot 0 , 5}{19 , 62}$
${x}_{\max} = \frac{8}{19 , 62}$
${x}_{\max} \cong 0 , 408 \text{ m}$