Final answer:
The maximum height of the function h(t) = 60t - 16t² can be found by calculating the vertex of the parabola. The time at which maximum height is reached is 1.875 seconds, and substituting it back into the equation gives the maximum height in meters.
Step-by-step explanation:
To find the maximum height of the function h(t) = 60t - 16t², we need to determine the vertex of the parabola represented by this quadratic equation as it models the motion under gravity, ignoring air resistance. Since the coefficient of t² is negative, the parabola opens downward, meaning the vertex gives the maximum height. The vertex can be found using the formula t = -b/(2a), where a is the coefficient of t² and b is the coefficient of t in the equation. For h(t) = 60t - 16t², a = -16 and b = 60. Plugging these into the vertex formula gives t = -60/(2*(-16)) = 60/32. Simplifying, we get t = 1.875 seconds. To find the maximum height, we substitute t = 1.875 back into the equation: h(1.875) = 60 * 1.875 - 16 * (1.875)². Calculating this gives a maximum height, which is the content loaded Fraction for this problem.