How Does a Horse's Size Influence Its Maximum Speed?

[bcjochim07]

Homework Statement

Estimate the maximum speed of a horse. Assume that a horse is 1.8 m tall and .5 m wide.

Homework Equations

The Attempt at a Solution

This problem is from the work & energy chapter in my book. However, I can't figure out the relevance of the dimensions of the horse. I don't even know where to start. Does this have something to do with horsepower? I'm confused.

 

[bcjochim07]

Hmmm... the dimensions probably have to do with the force of drag:

(1/4)(.9 m^2)v^2= Drag

So, the only force acting on the horse is drag:

Drag= (.225)v^2

P= Fvcostheta

So maybe the power of a horse is 1hp? 1hp = 746 W
746W= .225*v^2 * v
746 J/s = .225 v^3
v=14.9 m/s ?