2. A cannonball is fired at an angle 0 = 35° to the horizontal, with a velocity

of 85 ms 1.

a) What is the maximum vertical height reached by the cannonball?

b) What is the maximum horizontal range of the cannonball?

a) 120 m

b) 690 m

Explanation:

Given:

x₀ = 0 m

y₀ = 0 m

v₀ = 85 m/s

θ = 35°

aₓ = 0 m/s²

aᵧ = - 9.8 m/s²

a) At the maximum height, the vertical velocity vᵧ = 0 m/s. Find y.

vᵧ² = v₀ᵧ² + 2aᵧ (y - y₀)

(0 m/s) ² = (85 sin 35° m/s) ² + 2 (-9.8 m/s²) (y - 0 m)

y ≈ 120 m

b) At the maximum range, the cannonball lands, so y = 0.

First, we need to find the time it takes to land.

y = y₀ + v₀ᵧ t + ½ aᵧ t²

(0 m) = (0 m) + (85 sin 35° m/s) t + ½ (-9.8 m/s²) t²

t = 0 s, 9.95 s

Now find the final horizontal position x:

x = x₀ + v₀ₓ t + ½ aₓ t²

x = (0 m) + (85 cos 35° m/s) (9.95 s) + ½ (0 m/s²) (9.95 s) ²

x ≈ 690 m