Question

We are standing on the top of a 1008 feet tall building and launch a small object upward. The object's vertical position, measured in feet, after t seconds is h(t)=-16t²+288t+1008. What is the highest point that the object reaches?

Answer 1

The highest point the object reaches, determined by the vertex of the parabolic function, is 2352 feet at 9 seconds after launch.

Step-by-step explanation:

The highest point that the object reaches is the vertex of the parabolic function given by h(t) = -16t² + 288t + 1008. To find the time at which the object reaches its maximum height, we use the formula t = -b/(2a) for the vertex of a parabola ax² + bx + c. In this case, a = -16 and b = 288, so t = -288 / (2 × -16) = 9 seconds. Plugging this back into the original equation gives us the highest point, h(9) = -16(9)² + 288(9) + 1008.

Calculating the value, we find that the highest point h(9) is 2352 feet.