Solve UROV Fluid Mechanics Homework: Max Vel, Time, Distance, Drag Force

[chrispet]

Homework Statement

Im working with a UROV and I have a technical scenario that I am supposed to solve. It seems pretty easy but i keep getting ridiculous answers.

Assuming a max thrust of 5 N for 1 motor/propeller, for the forward direction only, use the above information to determine the Max Velocity, the Time to achieve this velocity and the Distance traveled. Please be sure to state all assumptions.
Calculate the Drag Force at Max Velocity

My robot has 2 thrusters thrusting forward and 1 upward, it weighs 5.68 lbs, and we are testing them a chlorine pool.
[/B]

Homework Equations

for the forward direction only, use the above information to determine the Max Velocity, the Time to achieve this velocity and the Distance traveled. Please be sure to state all assumptions.
Calculate the Drag Force at Max Velocity[/B]

The Attempt at a Solution

I was trying to use F=ma to get the acceleration then use constant accel equations to get the other parts but I think there's too many unkowns.
I had 2 equations,
F = ma(horizontal) = 2T - Fd
F = ma(vertical) = T - Fd - W

T = 5 (thrust)
W = 5.68 lbs = 25.27 N
m = .1765 slugs = 2.576 kg[/B]

assuming: the drag forces in both directions are equal, and the accel in the horizontal is equal to 2x the accel in the vertical. With this i got a(horizontal) = 23.5 m/s^2

this is obviously ridiculous so i didnt continue, and even if i did i couldn't get much further because i have too many unknowns too solve any constant accel equations. Any help please?

 

[haruspex]

There are several problems with your analysis.
Drag does not operate independently in each ordinate. It depends on the overall speed. Not sure what the vertical thruster is doing, though. Is it only there to counteract gravity, or is it also delivering 5N thrust? If the latter, we need to know the buoyant force too. If it is only to maintain constant height, we can ignore it and treat it as purely a one dimensional problem.

You seem to have calculated an acceleration, not a velocity, and I do not see anywhere that you have taken drag into account. You need an expression that specifies the drag as a function of speed.