Final answer:
To determine the time to reach maximum height, the vertex formula t = -b/(2a) is used, yielding 2 seconds. The maximum height is found by substituting this time into s(t) = -16t^2 + 64t, resulting in 64 feet. Hence, answer A is correct.
Step-by-step explanation:
If an object is projected upward from ground level with an initial velocity of 64 ft per sec, its height after t seconds is given by the equation s(t) = -16t^2 + 64t. To find the time it takes to reach its maximum height, we need to identify the vertex of this parabolic equation, recognizing that the coefficient of the t^2 term is negative, indicating that the parabola opens downward, hence the vertex of this parabola gives the maximum height.
The time at which the object reaches its maximum height can be found by using the formula t = -b/(2a), where a is the coefficient of t^2 and b is the coefficient of t. In our equation, a = -16 and b = 64, so we plug these values in to get t = -64/(2 * -16) = 2 seconds.
To find the maximum height, we substitute t = 2 back into the original equation to get s(2) = -16(2)^2 + 64(2) = -64 + 128 = 64 feet. Therefore, the answer is A) It will take 2 seconds to reach the maximum height, and the maximum height is 64 feet.