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nautikal
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Homework Statement
A baseball is thrown straight up. The drag force is proportional to v[tex]^{2}[/tex]. In terms of g, what is the ball's acceleration when its speed is half its terminal speed and a) it is moving up? b) it is moving back down?
Homework Equations
[tex]\sum F=ma[/tex]
[tex]mg + bv^{2}=ma[/tex] - When the ball is moving up
[tex]mg - bv^{2}=ma[/tex] - When the ball is moving back down
The Attempt at a Solution
We did something like this in class except we used [tex]mg - kv=ma[/tex]. We went through the calculus and got an equation for v(t) and then took the derivative to get a(t). Following my notes, I did the calculus to get an equation for v(t), and then I took the derivative to get an equation for a(t) using [tex]mg - bv^{2}=ma[/tex]. Below is what I got (in the attachment). I haven't done calculus like this since last May, so there may be some errors, but that's what I got.
So I got an answer for a(t) for when the ball is moving down, but I don't know what to do in order to simplify it so that it's acceleration for "when its speed is half its terminal speed".
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