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## Homework Statement

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.

## Homework 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)

## 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!