# Homework Help: Speed of a sphere fired straight up, including quadratic air resistance

1. Mar 22, 2009

### soundbyte

1. The problem statement, all variables and given/known data
A sphere of radius 0.2 cm is fired straight up with speed v0. What is its speed when it hits the ground? (Include quadratic air resistance but ignore linear air resistance.)

2. Relevant equations
Quadratic air resistance: FR = cv2
c = 0.5CpA = 4.05 x 10-6

3. The attempt at a solution
I figured as the sphere rises, its velocity can be modeled as v = v0 - gt - cv2t/m. As it falls, velocity can be modeled as v = gt - cv2t/m. Other than that, I'm not really sure where to go.

2. Mar 23, 2009

### lanedance

Hi soundbyte, welcome to PF

I don't think you can write the velocity like that, as the equation

v = v0 + a.t is for constant acceleration only,

in this problem a varies with v and v=v(t), so a= a(t)...(ie a is a function of t)

A good place to start would be to write the acceleration on the sphere as a function of v based on the forces