Suppose a free falling particle of m = 1 with initial conditions y(t = 0) = 0 and
~v(t = 0) = 2ˆj (suppose that g = 1).
(i)Find the potential energy
(ii) What is the initial total energy
(iii) Find the function of the velocity with respect to the position (height)
(iv) Find the maximum height that the particle will reach
(v) Solve (iv) using Newtons equations