Question

what effect does increasing the launch angle of a projectile launched from ground level have on its range when it lands? (1 point)
increasing the launch angle has no effect on the range.
increasing the launch angle increases the range.
increasing the launch angle increases the range if the initial angle is less than 45 degrees, but decreases the range if the initial angle is more than 45 degrees.
increasing the launch angle decreases the range.

Explanation:

The range formula for a projectile launched from ground - level is $R=\frac{v_{0}^{2}\sin2\theta}{g}$, where $v_{0}$ is the initial velocity, $\theta$ is the launch - angle, and $g$ is the acceleration due to gravity. The function $y = \sin2\theta$ has a maximum value of 1 when $2\theta = 90^{\circ}$ (i.e., $\theta=45^{\circ}$). When $\theta<45^{\circ}$, increasing $\theta$ increases $\sin2\theta$ and thus the range. When $\theta > 45^{\circ}$, increasing $\theta$ decreases $\sin2\theta$ and thus the range.

Answer:

Increasing the launch angle increases the range if the initial angle is less than 45 degrees, but decreases the range if the initial angle is more than 45 degrees.