How to Solve for an Object's KE and Heat in a Differential Equations Problem?

[steven452]

Homework Statement

We're supposed to find the object's KE and heat. Given:

Forces on Object: Air Drag + Gravity
Air Drag = .5(coefficient of drag)(1.2 kg/m³)v²A
A = cross sectional area
R = Radius of object
Object is X Km above the ground
Initial velocity = V

We are told it should be an initial value problem.

Homework Equations

Possibly y"+ (Force due to Drag)y' + (gravity)y = 0

The Attempt at a Solution

I tried plugging in the initial conditions to the equation above, but I'm stuck at that point.

 

[JaWiB]

Possibly y"+ (Force due to Drag)y' + (gravity)y = 0

How did you get that equation?

Since kinetic energy has nothing to do (directly) with position, you shouldn't have to solve for y (which I'm assuming stands for the height of the object); instead, focus on v(t), and don't forget that a(t) = dv/dt

 

[steven452]

I just sort of assumed that's the equation we had to use, but I wasn't sure?

What initial value differential equation should I be using?

 

[JaWiB]

You should be able to derive an equation using Newton's second law and what you know about the forces acting on the object

 

[steven452]

I was originally going to do it entirely with Newton's laws, but I'm having a hard time seeing how Newton's equations can "convert" into DE?