The range of a projectile fired at an angle with the horizontal and with an initial velocity of feet per second is where r is measured in feet. A golfer strikes a golfball at 80 feet per second. Ignoring the effects of air resistence, at what angle must the golfer hit the ball so that it travels 110 feet? (Round answer to nearest angle.)

Question

The range of a projectile fired at an angle  with the horizontal and with an initial velocity of  feet per second is  where r is measured in feet. A golfer strikes a golfball at 80 feet per second. Ignoring the effects of air resistence, at what angle must the golfer hit the ball so that it travels 110 feet? (Round answer to nearest angle.)

Quizplus · Accepted Answer

Using the formula $r=\frac{v_0^2\sin2	heta}{g}$, where $v_0$ is the initial velocity, $	heta$ is the angle of projection, $g$ is the acceleration due to gravity, and $r$ is the range, we can solve for $	heta$.
Plugging in the given values of $v_0=80$ and $r=110$ and the known value of $g=32.2$ feet per second squared, we get:
$$110=\frac{80^2\sin2	heta}{32.2}$$
$$\sin2	heta=\frac{110	imes 32.2}{80^2}=0.2175$$
Using the identity $\sin2	heta=2\sin	heta\cos	heta$, we can rewrite this as:
$$2\sin	heta\cos	heta=0.2175$$
Since $\sin	heta$ and $\cos	heta$ are both between 0 and 1, we know that $2\sin	heta\cos	heta$ is also between 0 and 1. Therefore, the solution to this equation must be an angle whose sine is between 0 and 1.
We can use the inverse sine function to solve for $	heta$:
$$	heta=\frac{1}{2}\sin^{-1}(0.2175)\approx 13.2^\circ$$
Rounding to the nearest degree, we get $	heta\approx 13^\circ$. Therefore, the answer is choice B.

The Range of a Projectile Fired at an Angle