Answer
In degrees,
θ = 36.87°
In radians,
θ = 0.205π radians
Step-by-step explanation
We are given the range as 300 feet.
Initial velocity = v₀ = 100 feet per second
We are told that the range is related to the initial velocity and the angle of batting to the horizontal, θ, through the expression
r = (v₀² Sin 2θ)/32
We can then insert the given parameters
r = (v₀² Sin 2θ)/32
300 = (100² Sin 2θ)/32
We can rewrite this as
10000 Sin 2θ = (300) (32)
Sin 2θ = (9600/10000)
Sin 2θ = 0.96
2θ = Sin⁻¹ (0.96)
2θ = 73.74°
Divide both sides by 2
(2θ/2) = (73.74°/2)
θ = 36.87°
In radians,
θ = 0.205π radians
Hope this Helps!!!