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## Homework Statement

A cannon is located on a cliff of height h. If the muzzle velocity of a projectile is v

_{0}, find the range of the projectile when the drag is proportional to the velocity.

## Homework Equations

ma=-mg-kv

_{y}. Vertical motion

ma=-kv

_{x}. Horizontal motion

mg=kv

_{t}. Terminal velocity

## The Attempt at a Solution

I first attempted to find t via the horizontal motion formula, but my answer doesn't take into account the height difference. Then I tried integrating the vertical motion equation and got an answer of

t=-v

_{t}/g * ln((v

_{t}+v

_{y})/(v

_{t}+v

_{oy})) where v

_{oy}is the initial vertical velocity. I then made v

_{y}=dy/dt and tried to find t from there but I have no idea how to do the integration.

Am I even on the right path? I'm hoping if I can find the time t given y I can plug that into xcosθ*t to give me the range.