1. The problem statement, all variables and given/known data A small rock is thrown vertically upward with a speed of 17.0m/s from the edge of the roof of a 30.0m tall building. The rock doesn't hit the building on its way back down and lands in the street below. Air resistance can be neglected. 2. Relevant equations Acceleration of gravity = 9.81m/s^2 The normal way: v^2 = u^2 + 2as v=u+a*t http://answers.yahoo.com/question/index?qid=20120204155622AAIs1sA How I want to do it: dv/dt = a(t) ds/dt = v(t) 3. The attempt at a solution a(t) = -9.8 m/s^2 v(t) = -9.8t m/s + C(m/s) 17 = -9.8*0 + C, C=17 v(t) = -9.8t(m/s) + 17(m/s) s(t) = -4.9t^2 + 17t + C 30 = -4.9*0 + 17*0 + C C = 30 s(t) = -4.9t^2+17t+30 -30 = -4.9t^2+17t+30 t=5.64s for part B. For part A, this would make it -9.8*5.64 + 17 = -38.272. My answers are wrong. Using the equations listed at Yahoo answers: v=(17^2+2*9.81*30)^(1/2)=29.6m/s and 29.62=-17+9.81*t, t=4.76s I'm certain there's a way to solve this as initial value problems. I'd rather get my calculus on than try to memorize these equations!