Question

A young girl standing on a cliff is throwing stones up into the air so that they land in the ocean below. The height h in meters of each stone above the ocean is realted to the time t in seconds after it has been thrown by the function h=-2t^2+2t+40. What is the maximum height reached by each stone?

A. 40.5m
B. 5m
C. 0.5m
D. 40 m

Answer 1

The maximum height reached by each stone is 40.5 meters.

Step-by-step explanation:

To find the maximum height reached by the stone, we need to determine the vertex of the quadratic function h=-2t^2+2t+40. The vertex represents the maximum or minimum point of the function. The vertex of a quadratic function with the equation h = at^2 + bt + c is given by the formula t = -b / (2a). In this case, a = -2 and b = 2, so the vertex is at t = -2 / (2*-2) = 0.5 seconds. To find the maximum height, we substitute t = 0.5 seconds into the equation h = -2t^2 + 2t + 40: h = -2(0.5)^2 + 2(0.5) + 40 = 40.5 meters.