Answer: To calculate the maximum height reached by the cannonball, we can use the equations of motion for vertical motion under gravity.
Given:
Initial velocity (u) = 40 m/s (upward)
Final velocity (v) = 0 m/s (at the maximum height, the velocity becomes zero)
Acceleration due to gravity (g) = 9.81 m/s² (downward, as it opposes the upward motion)
The general equation for the vertical motion is:
v² = u² + 2 * g * s
where:
v = final velocity
u = initial velocity
g = acceleration due to gravity
s = displacement (in this case, the maximum height reached)
At the maximum height, the final velocity is 0 m/s, so the equation becomes:
0 = 40² + 2 * (-9.81) * s
Now, let's solve for s (the maximum height):
0 = 1600 - 19.62 * s
19.62 * s = 1600
s = 1600 / 19.62 ≈ 81.47 meters
The maximum height reached by the cannonball is approximately 81.47 meters.