Final answer:
The maximum height that the ball will reach is 6.25 meters.
Step-by-step explanation:
The maximum height that the ball will reach can be found by finding the vertex of the quadratic function representing the height of the ball. The function is given as h(t) = -16t^2 + vt, where v is the initial velocity of the ball. The maximum height is achieved at the vertex, which is the t-coordinate of the vertex can be found using the formula t = -b/2a, where a = -16 and b = v. Plugging in the given initial velocity of 20 m/s, we get t = -20/2(-16) = 0.625 s. Plugging this value of t back into the function gives us the maximum height: h(0.625) = -16(0.625)^2 + 20(0.625) = 6.25 m.