Question

The horizontal distance covered by a projectile fired with an initial velocity $v$ at an angle $\theta$ with the horizontal, is given by
$H(v,\theta )=\frac{v^2\sin \left(2\theta \right)}{32}$
If a ball is kicked with an initial velocity of $30$ feet per second at an angle of $50$ degrees with the horizontal, find the horizontal distance, in feet, from the point where the football is kicked to the point where the football first hits the ground.

• A. $28$
• B. $30$
• C. $33$
• D. $36$
• E. $39$

Answer 1

The correct option is A $28$

Given, $H(v,\theta )=\frac{v^2\sin 2\theta }{32}$

Here $v=30$ feet per second, angle $\theta =50$

$H(v,\theta =\frac{\left(30{)}^2\sin \right(2\times 50)}{32}$

$=$ $\frac{900\sin 100}{32}$

$=$ $\frac{900\times 0.9848}{32}=27.70\approx 28$