A pelican flying along a horizontal path drops a fish from a height of 7.0 m. The fish travels 8.0 m horizontally before
it hits the water below. What is the pelican's speed?

time for fish to fall 5.4 m = √2d/g = √(2)(5.4)/9.81 = √1.100917 = 1.0492 s

pelican's initial speed = horizontal fish speed = 8.0/1.0492 = 7.6 m/s ANS a)

time for fish to fall 2.7 m = √2d/g = √0.55046 = 0.7419 s

fish travels a distance = speed x time =  (7.6)(0.7419) = 5.6 m ANS b)

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .