Calculating Y-Component of Acceleration for a Thrown Ball

[clarineterr]

Homework Statement

A baseball is thrown straight up. The drag force is proportional to v^{2}.
In terms of g, what is the y-component of the ball's acceleration when its speed is half its terminal speed and it is moving up? In terms of g, what is the y-component of the ball's acceleration when its speed is half its terminal speed and it is moving back down?

Homework Equations

v terminal = $$\sqrt{mg/D}$$

The Attempt at a Solution

I honestly have no idea how to attempt this problem

 

[RoyalCat]

The drag force is of the form:
$$F_d = -kv^2$$

Or to use your notation:
$$F_d = -Dv^2$$

The terminal velocity is achieved when the ball starts falling at a constant velocity. At that point, the following holds true:
$$kv^2=mg$$

 

[tiny-tim]

I honestly have no idea how to attempt this problem

Hi clarineterr!

Start "acceleration = dv/dt = … "