Question

A coin, thrown upward at time t=0 from an office in the Empire State Building, has height in feet above the ground t seconds later given by h(t)=−16t²+64t+960=−16(t−10)(t+6). Determine the time at which the coin reaches its highest point.

Answer 1

The coin reaches its highest point 2 seconds after being thrown upward.

Step-by-step explanation:

To determine the time at which the coin reaches its highest point, we need to find the vertex of the parabolic function that represents the height of the coin. The vertex occurs at the maximum height of the parabola. In this case, the height function is given as h(t) = -16t^2 + 64t + 960. To find the time of the vertex, we can use the formula t = -b / (2a), where a = -16 and b = 64. Plugging in these values, we get:

t = -64 / (2(-16))

t = 2 seconds

Therefore, the coin reaches its highest point at 2 seconds after being thrown upward.