Final answer:
To find the maximum height of an object with the height function h = 116t - 16t², we calculate the vertex of the parabola. The time at which the maximum height occurs is found by setting the derivative of the function to zero, and then substituting this time back into the original function to find the height, which is 145 feet (Option D)
Step-by-step explanation:
To find the maximum height reached by an object tossed vertically upward with a height function given by h = 116t - 16t², we need to find the vertex of the parabola represented by this function. Since the coefficient of t² is negative, the parabola opens downwards, and the vertex will give us the maximum height.
To find the time at which the maximum height is reached, we take the derivative of the height function with respect to time (dh/dt) and set it to zero. So, dh/dt = 116 - 32t = 0. Solving for t yields t = 116/32 = 3.625 seconds. Substituting this value back into the height function, we get h = 116(3.625) - 16(3.625)². Calculating this gives us the maximum height, which is 145 feet (option D).