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I was recently intrigued by the site: http://www.lcse.umn.edu/specs/labs/catapult/ which sets about showing a computational solution to the problem of projectile motion with air resistance. I think the site is a great idea, and presented well, but it seems like some of the physics just has to be wrong (their equations are right down the bottom of the page.) Its entirely probable that I'm just misunderstanding it myself, and I'm hoping someone on here can help sort me out. My problem is this:

They solve the problem by dividing the velocity and acceleration into two vectors, and solving for each separately; so velocity v becomes v(x) and v(y), acceleration a becomes a(x) and a(y). Their equation for a(y) reads:

a(y) = (mg - bv(y)^2)/m

where m=mass, g=gravity, and b=drag coefficient. Assuming the usual orientation (positive y is up; negative down) g is presumably a negative number in whatever units pleases you most. But this being the case, then wether the projectile is going up or down (v(y) positive or negative) -bv(y)^2 willalwaysbe negative. Which means that air resistance slows the projectile down on its way up - I'm with you so far - andspeeds it upon the way back down. Which can't be right, can it?

Can anyone point out where I've got it wrong, or suggest how to fix the equation if I've got it right? Is it just a matter of adjusting the sign of the drag portion of the equation to always oppose the direction of travel?

Thanks for any advice,

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# Mechanics: projectile motion with air resistance

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