Abox slides on an inclined plane (=40°) that has friction (=0.43) which causes the box to slide with a constant velocity of 3 m/s. the box reaches the bottom and continues to slide across a horizontal surface with friction (=0.34) until coming to rest five meters from the base of the ramp. what is the length of the ramp that the box slid down?

the answer is that the length of the ramp is 4m, but i don't see how to get there. since the box is sliding down the ramp at a constant speed, there is no net force acting on the box, which means the net work done on the ramp is zero. the energy the box has at the bottom of the ramp doesn't equal the work done to travel 5 meters from the bottom of the ramp.

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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 .