What is a differential equation?

[KAV]

Homework Statement

A skier of mass M is skiing down a frictionless hill that makes an angle θ with the horizontal. The skier starts from rest at time t = 0 and is subject to a velocity-dependent drag force due to air resistance of the form F = -bv, where v is the velocity of the skier and b is a positive constant. Express all algebraic answers in terms of M, b, θ , and fundamental constants.

Write a differential equation that can be used to solve for the velocity of the skier as a function of time.

Homework Equations

I understand a differential equation involves calculus, but I don't know how to apply it.

The Attempt at a Solution

v = (mgsinθ - ma)/b

 

[rock.freak667]

Try finding the resultant force, then use Newton's 2nd law with non-constant velocity, i.e. $F=m \frac{dv}{dt}$

 

[Andrew Mason]

Homework Statement

A skier of mass M is skiing down a frictionless hill that makes an angle θ with the horizontal. The skier starts from rest at time t = 0 and is subject to a velocity-dependent drag force due to air resistance of the form F = -bv, where v is the velocity of the skier and b is a positive constant. Express all algebraic answers in terms of M, b, θ , and fundamental constants.

Write a differential equation that can be used to solve for the velocity of the skier as a function of time.

Homework Equations

I understand a differential equation involves calculus, but I don't know how to apply it.

The Attempt at a Solution

v = (mgsinθ - ma)/b

You have written the correct differential equation already. In differential form it would be:

$$m\frac{d^2s}{dt^2} = mgsin\theta - b\frac{ds}{dt}$$

A differential equation is just an equation containing differentials. The solution of these equations is often complicated. Certain techniques for solving them exist and are the subject of a course in differential equations.

AM