Two people, one of mass 78 kg and the other of mass 59 kg, sit in a rowboat of mass 88 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat 2.9 m apart from each other, now exchange seats. How far will the boat move?

The boat will move -0.24 m and the negative sign indicates left direction.

Explanation:

mass of people A = 78 kg

mass of people B = 59 kg

mass of rowboat = 88 kg

Let the displacement of the boat be x

                                        = 2.9 + x

                                        = -2.9 + x

As net external F = 0

                                ∑mx = 0

        88 (x) + 78 (2.9 + x ) + 59 (-2.9 + x) = 0

          88x + 226.2 + 78x - 171.1 + 59x = 0

         225x + 55.1 = 0

                           x = -55.1 / 225

                          x = -0.24

The negative sign indicates left direction.

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 .