Speed of a sphere fired straight up, including quadratic air resistance

[soundbyte]

Homework Statement

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.)

Homework Equations

Quadratic air resistance: F_R = cv²
c = 0.5CpA = 4.05 x 10^-6

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.

 

[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