AP Physics C: Solving Energy Homework Equation

[SHawking]

Homework Statement

First, this is not an assignment, per se, it is for my own help, and If someone could help me work it through that would be much appreciated.

An object of mass 1 Kg is launched at an angle of 42° from the horizontal at 180 m/s. A force of drag acts on it that is dependent on its velocity, with the force being equal to -.012V. What energy does the ball have when it reaches its maximum height?

Homework Equations

I solved the initial components in both the x and y directions and got 133.8 m/s and 120 m/s.
Other equations:
E=K+U
K=.5mv^2
U=mgh
x(t)=x+(integral)v(t)dt
I am sure I am missing some, which is part of my problem.

The Attempt at a Solution

I started with F=mdv/dt
Integrated to
Integral from Vi to V (dv')/fv'=t/m which didnt help much.
I then tried
mdv/dt=mg-kv (kv being my -.012v)
But, was having trouble with my signs, and it didnt look like it was coming out right.

THe retarding forces in the y direction are -mg-.012v
and the x direction is only -.012 v

Going to F=ma I tried various substitutions and again, had little luck.

I know I wiill need to solve the height at which the velociy is zero, using only the y component to get potential energy, and also find the x velcity at this time to get the kinetic energy and then add them up to get the total energy. The thing that is giving me difficult is the retarding force as a function of the velocity, so the force will be constantly changing.

If anyone could help that would be very much appreciated!

 

[SHawking]

I have been working on it, and got stuck, though it seems like this route would work.
Using F=ma and trying to solve for the downward force in the y direction I get
F=-mg-.012v
F=-mg-.012(dx/dt)
Integral of F dt= -mg-integral .12 dx
From the looks of this, I think that setting up the differential equation was not the right step, and am still unsure where to go from here.

 

[SHawking]

Could someone assure me that this problem is possible with the given information. I keep getting two variables, both unknown and no good substitutions.