An object with the mass 2 kg slides on a frictionless surface. When the velocity of the object is h, the object is subjected to a force (air resistance) that's $5v^2$ N.
Apparently the equation is
$$ F = ma = m\frac{dv}{dt} = -5v^2 $$
I do understand how to solve this differential equation. What I don't understand is why the downwards force is equal to air resistance?
Edit: Forgot to mention that v(0) = 3.
Best Answer
The velocity is horizontal. We might as well call it along the $+x$ axis. The air resistance is opposite the velocity, so is in the $-x$ direction, horizontal. You now have $F=m\frac {dv}{dt}=-5v^2$ The equation separates-can you solve it?