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

Question

Physics

Aryanna Hurley

25 July, 16:56

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

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Roman Newton · 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°