Final answer:
To find the highest point of the cannonball's trajectory, we need to determine the vertex of the parabolic function. The time it takes for the cannonball to reach its highest point is t = 3.79 seconds.
Step-by-step explanation:
To find the highest point of the cannonball's trajectory, we need to determine the vertex of the parabolic function. The given function h(t) = -16t^2 + 300t represents the height of the cannonball in feet at time t seconds after it is shot.
The vertex of a parabolic function in the form h(t) = at^2 + bt + c is given by the formula t = -b/2a. In this case, a = -16 and b = 300. Plugging in these values, we can find the time it takes for the cannonball to reach its highest point.
Using the quadratic formula yields two possible values for t: t = 3.79 seconds and t = 0.54 seconds. Since the ball is at a height of 10 feet at two times during its trajectory - once on the way up and once on the way down - we take the longer solution for the time it takes the ball to reach the spectator, which is t = 3.79 seconds.