How to solve for v

Question

I am trying to solve for v in this equation.

$(v/g)(ksin\theta + v)(1 - e^{-gt/v}) - vt = 0$

EDIT: Does it help if I also have the fact that $((kvcos\theta)/g)(1-e^{-gt/v}) -x = 0$? Every variable except $v$ is known in both.

Answer 1

After your edit you can do the following:

From the second equation extract: $$ (1-e^{-\frac{gt}{v}}) = \frac{xg}{kv\cos\theta} $$ Pluging this back into the first equation and we get: $$ \frac{v}{g}(k\sin\theta+v)\frac{xg}{kv\cos\theta}-vt = 0 $$ Assuming that $ v \neq 0 $ you get that $v$ is: $$ v = \frac{xk\sin\theta}{kt\cos\theta-x} $$