Question

Now, let’s see what happens when the cannon is high above the ground. click on the wheel of the cannon, and drag it upward as far as it goes (about 21 m above the ground). set the initial velocity to 20 m/s, and fire several balls while varying the angle.for what angle is the range the greatest

Answer 1

The equation for range is:

R = v₀²sin(2θ)/g
To find the maximum R, differentiate the equation and equate to zero. The solution is as follows:

dR/dθ = (v₀²/g)(sin 2θ)
dR/dθ = (v₀²/g)(cos 2θ)(2) = 0
cos 2θ = 0
2θ = cos⁻¹ 0 = 90
θ = 90/2
θ = 45°