# Resisted vertical projectiles

My textbook writes this equation for the vertical acceleration of a particle undergoing 2D resisted projectile motion (the resistance is linearly proportional to velocity).

The situation is simply the particle being shot up at an acute angle, with upward as positive, k>0.

My question is...shouldn't there be two vertical acceleration equations for the particle? One for when it travels upwards, and one for when it travels downwards? If so, why is only this equation for vertical acceleration given? From my point of view, this equation only represents the vertical acceleration of the particle as it moves upward.

I suspect I am not really getting the signs positive or negative right in my head??

The equation is valid for the projectile going up or down. When going up, $$\dot y>0$$, and so air resistance should point down: $$-k\dot y<0$$. When going down, $$\dot y<0$$, and so air resistance should point up: $$-k\dot y>0$$.
The force of gravity is always down, hence $$-g<0$$ always.
If the air resistance force is proportional to the squared speed, then you do need to be careful with your signs, since then $$(\dot y)^2$$ is nonnegative no matter the sign of $$\dot y$$.