Answer
In degrees,
θ = 1.91°
In radians
θ = 0.0106π radians
Step-by-step explanation
We are provided with the following parameters
Range = r = 1000 yards
1 yard = 3 feet
1000 yards = 3000 feet
Range = r = 3000 yards
Initial velocity = v₀ = 1200 feet per second
Angle of elevation = θ = ?
We are then told they are all related through the expression
r = (v₀² Sin 2θ)/32
Inserting the parameters,
r = (v₀² Sin 2θ)/32
3000 = (1200² Sin 2θ)/32
We can rewrite this expression as
1200² Sin 2θ = (3000) (32)
1440000 Sin 2θ = 96000
Sin 2θ = (96000/1440000)
Sin 2θ = 0.0667
2θ = Sin⁻¹ (0.0667)
2θ = 3.82°
Divide both sides by 2
(2θ/2) = (3.82°/2)
θ = 1.91°
In radians
θ = 0.0106π radians
Hope this Helps!!!