Final answer:
The cannonball reaches its highest point of 1406.25 feet, 9.375 seconds after being shot. This is calculated using the vertex formula of a parabola derived from the quadratic equation for height of the projectile.
Step-by-step explanation:
To find the highest point of a projectile's trajectory and the time it takes to reach that point, we can use the vertex of the parabolic path described by the quadratic equation for height. The provided equation seems to have a typo, but it should be in the form of a parabolic equation h(t) = -16t^2 + (initial velocity in the vertical direction)t. If the initial velocity can be assumed to be 300 ft/s based on the provided information, the equation for height is h(t) = -16t^2 + 300t. To find the time when the cannonball reaches the highest point, we need to find the vertex of the parabola. The vertex form of a parabola is h(t) = a(t-h)^2 + k, where (h, k) is the vertex of the parabola. The time t at which the projectile reaches its maximum height is given by -b/(2a), where a is the coefficient of t^2 and b is the coefficient of t in the original quadratic equation. In this case, a = -16 and b = 300, so the time to reach the maximum height is t = -300/(2(-16)) = 9.375 seconds. Substituting t = 9.375 into the equation h(t), we get the maximum height: h(9.375) = -16(9.375)^2 + 300(9.375) = 1406.25 feet. So, the cannonball reaches its highest point at 1406.25 feet, 9.375 seconds after it is shot.