How Do You Calculate Ymax and Velocity at Half Ymax Using Energy Conservation?

[student 1]

Homework Statement

A ball is thrown vertically from y=0 with velocity V₀. Using only energy considerations, find the following
a. Y_max in terms of V₀.
B. The Velocity(V_1/2 at y= 1/2 Y_max (in terms of V₀

Homework Equations

K_i+U_i=K_f+U_f

The Attempt at a Solution

I'm not sure how to start this off to find the y_max in terms of V₀

 

[Dick]

The U in your problem is the potential energy mgy. The K is the kinetic (1/2)mv^2. At the initial time v=V0 and y=0. At the final time v=0 and y=ymax. Use your energy conservation to solve for ymax in terms of V0.