1. The problem statement, all variables and given/known data A ball is thrown straight upward and rises to a maximum height of y above its launch point. Show that the velocity of the ball has decreased to a factor α of its initial value, when the height is y2 above its launch point is given by y2=(1-α^2)y. Also SHOW that y2=(1-α^2)y. 2. Relevant equations y=vt+1/2at^2, where a=-9.8m/s^2 v1=v0+at (maybe) y2=(1-α^2)y 3. The attempt at a solution I've already attempted a solution that involves plugging in y=vt +1/2at^2 and did a bunch of algebra; I was writing so fast I probably did something illegal; one thing i was worried about was plugging in (v1-v0)/t for the acceleration, and canceled out the t^2. I also attempted a solution that involved looking at derivatives of both sides. That is, y2' = ((1-α^2)y)' with respect to t, after plugging in the aforementioned equation of kinematics. After all the algebra was said and done, I ended up with .5v(final)t+.5v(initial)t=y2, which definitely sounds incorrect to me. Is there a way to modify the kinematics equation y=vt+1/2at^2 to include y2?