(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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?

2. Relevant 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

3. 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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# Homework Help: Drag force (air resistance) and acceleration

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