Is This How Projectile Motion Is Described Using Differential Equations?

[cscott]

I this how you would describe projectile motion in terms of DE's?

$$\frac{dy}{dt} = 25.0 - gt$$
$$\frac{dx}{dt} = 10.0$$

 

[arildno]

No. For one, "g" doesn't equal 9.8 in most common choices of units.

 

[cscott]

No. For one, "g" doesn't equal 9.8 in most common choices of units.

Ok, well I changed it to "g". What else is wrong?

 

[dav2008]

Well if your initial velocities (25 and 10) are given in m/s then there's no problem of using 9.8 for g.

 

[cscott]

Well if your initial velocities (25 and 10) are given in m/s then there's no problem of using 9.8 for g.

That's what I intended.

 

[arildno]

I this how you would describe projectile motion in terms of DE's?

$$\frac{dy}{dt} = 25.0 - gt$$
$$\frac{dx}{dt} = 10.0$$

Consider your actual question. Nowhere did you state what 25.0 or 10.0 represent, and you wanted an answer for a GENERAL description of projectile motion in terms of D.E.
Thus, you ought to have written something like:

$$\frac{dy}{dt} = v_{0,y} - gt$$
$$\frac{dx}{dt} = v_{0,x}$$
where x(t), y(t) are horizontal and vertical positions as functions of time t, $\vec{v}_{0}=(v_{0,x},v_{0,y})$ is the initial velocity, and "g" is the acceleration due to gravity.

If you had written it as that, your equations would have been proper to your question.