what angle must an object be launched to achieve optimal range? 10 degrees 30 degrees 45 degrees 90 degrees

Explanation:

Step1: Recall range formula

The range formula for projectile motion is $R=\frac{v_{0}^{2}\sin(2\theta)}{g}$, where $v_{0}$ is the initial velocity, $\theta$ is the launch - angle, and $g$ is the acceleration due to gravity.

Step2: Maximize the sine function

The sine function $y = \sin(x)$ has a maximum value of 1. We want to maximize $\sin(2\theta)$. So, we set $\sin(2\theta)=1$.

Step3: Solve for $\theta$

If $\sin(2\theta)=1$, then $2\theta = 90^{\circ}$ (since the maximum of the sine function occurs at $90^{\circ}$ for the standard sine curve). Solving for $\theta$, we get $\theta = 45^{\circ}$.

Answer:

C. 45 degrees