A projectile is shot at an angle of pi/12  and a velocity of 54 m/s. How far away will the projectile land?

Apr 10, 2016

${x}_{m} = 148 , 62 \text{ m}$

Explanation:

$\text{the given data:}$
${v}_{i} = 54 \text{ " m/s" initial velocity}$
$\alpha = \frac{\pi}{12} \text{ angle}$
$2 \cdot \alpha = 2 \cdot \frac{\pi}{12} = \frac{\pi}{6}$
$\sin \left(\frac{\pi}{6}\right) = 0 , 5$
$g = 9 , 81 \text{ } \frac{m}{s} ^ 2$

${x}_{m} = \frac{{v}_{i}^{2} \cdot \sin 2 \alpha}{g}$

${x}_{m} = \frac{{54}^{2} \cdot 0 , 5}{9 , 81}$

${x}_{m} = 148 , 62 \text{ m}$