Projectile velocity as a function of angle

Question

A batted baseball leaves the bat at an angle θ with the horizontal and an initial velocity of v₀ = 100 feet per second. The ball is caught by an outfielder 300 feet from home plate. Find θ if the range r of a projectile is give by r= (1/32)v²₀ sin2θ

Answer 1

R = range = 300 ft

 

R = v₀²sin(2θ) / g

 

sin(2θ) = gR/v₀² = (32)(300)/(100²) = 0.96

 

θ = (1/2)sin^-1(0.96) = 36.87º