To determine the initial position of the water bottle, we can assume that Thor throws the bottle at time t=0. Since Thor is 5.5 feet above the ground, the initial position of the water bottle is 5.5 feet above the ground.
To find the maximum height the bottle can reach, we need to find the vertex of the quadratic function h=-16t^2+32t. The vertex of a quadratic function with the form h = at^2 + bt + c is given by the x-coordinate of the vertex, which is given by the formula x = -b/(2a). In this case, a=-16 and b=32, so the x-coordinate of the vertex is -32/(2*-16) = 1.
To find the corresponding y-coordinate (maximum height), we substitute t=1 into the equation h=-16t^2+32t: h = -16(1)^2 + 32(1) = 16 feet.
Therefore, the maximum height the bottle can reach is 16 feet.
Since the initial position of the water bottle is 5.5 feet above the ground and the maximum height is 16 feet, Luther will be able to reach the bottle since it will be above his location on the ledge.