The Phenomenon: Christine throws a ball straight up, letting go of the ball at a height of yi above the ground. When she lets go, the ball has an initial speed vi. The ball travels straight up to its maximum height ymax and falls back down. Assume the frictional effects from air resistance are insignificant. Constructing a particular model to find the maximum height:

a) Construct a particular model of this phenomenon that can be used to determine the maximum height of the ball. (yf = ymax). Sketch of the path of the ball and a complete Energy-System Diagram (with accompanying energy conservation equation). What do you know about the ball’s speed at its maximum height when it’s thrown straight up? How do you know this?

b) Indicate the initial and final positions of the ball on your sketch that correspond to the initial and final conditions in your Energy-System Diagram.

c) Rewrite the energy conservation equation by replacing the two terms with algebraic expressions for the changes in energy of the energy systems. Does the resulting algebraic sign of each term in your energy conservation equation agree with the increases and decreases in energy systems in your diagrams?

d) Solve the equation for (∆y = yf - yi). Does the sign of(∆y = yf - yi) make sense for this particular physical situation?