The range of a projectile fired at an angle θ with the horizontal and with an initial velocity of v 0 feet per second is r = 1 v 20 sin 2θ where r is measured in feet. a golfer strikes a golf ball at 120 feet per second. 32 ignoring the effects of air resistance, at what angle must the golfer hit the ball so that it travels 140 feet? (round answer to nearest angle.)

Projectile motion is characterized by a motion that has two vector forces: the velocity along the x and y directions. As a result, the motion follows an arc-shaped direction. These two directions are actually independent of each other. 

There are already derived equations for this so it is already convenient. However, your given equation for range is incomplete. The correct equation is:

R = v₀²sin2θ/g

where
R = 140 ft
v₀ = 120 ft/s
g = 32.2 m/s²

Substituting the values,

sin 2θ = Rg/v₀²
sin 2θ = (140)(32.2)/(120²)
sin 2θ = 0.313
2θ = sin ⁻¹ (0.313)
2θ = 18.24°
θ =18.24°/2
θ = 9.12°

With a continuous thought process.