Final answer:
Using the equation g(t) = -5t² + 20t + 2, the maximum height the cannonball reaches is found to be 22 meters, which is greater than the castle wall's height of 21 meters. Thus, the cannonball will clear the wall.
Step-by-step explanation:
To determine if the cannonball can clear the 21-meter high castle wall based on the provided equation g(t) = -5t² + 20t + 2, we must find the maximum height reached by the ball. This can be found by calculating the time at which the height is maximum, which is the vertex of the parabola represented by the equation. The maximum height is the value of g(t) at the vertex, which is the time t at which the derivative of g(t) is zero. However, we can also use the formula -b/2a where a is the coefficient of t² and b is the coefficient of t. Here, a is -5, and b is 20, so the time at which maximum height is reached is -20/(2·(-5)) = 2 seconds.Plugging this time back into the equation gives us the maximum height: g(2) = -5(2)² + 20(2) + 2 = -20 + 40 + 2 = 22 meters. Since this maximum height of 22 meters is greater than the 21-meter high castle wall, the cannonball will indeed clear the wall.