Help!!
A 0.368 kg bead can slide on a curved wire as seen in the figure.
Assume h1 = 4.20 m and h2 = 2.14 m. If the wire is frictionless and the bead is released with an initial speed of 1.96 m/s in the forward direction then find the speed of the bead at B.
If the wire is frictionless, find the speed of the bead at C.

The velocity at B is    

The velocity at C is  

Explanation:

From the question we are told that

     The mass of the bead is

     The first height is  

      The second height is  

      The initial speed of the bead is  

According to the law of energy conservation

Now is the kinetic energy at A and it is mathematically represented as

          is the potential energy at A which is mathematically represented as

        is the kinetic energy at B which is mathematically represented as

Where v is the speed of the bead at B

            is the potential energy at B which equal to 0 because height is  0 at B

So

Making v the subject

substituting values

According to the law of energy conservation

So

is the kinetic energy at c which is mathematically represented as

  is the potential energy at C which is mathematically represented as

So

making the subject

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 .