Assuming the object begins its motion from rest, and at an initial height h from the surface of the earth: a) calculate the velocity of the object as a function of time using the laplace transform approach. b) does the object reach a terminal velocity? if so, what is this terminal velocity? note that the terminal velocity is the (constant) velocity reached after a sufficiently large time. c) compare the solution obtained for velocity in a) with the solution for the case where b = 0 (free fall under gravity without friction). provide rough sketches of the solutions for both cases.

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 .

0.93xc=0.93x3x10^8m/s

2.54cm is 1 inch

360seconds i 1 hr