Max Boat Speed w/ 2 Engines: Proportional to v^2 Resistive Force

[Myopical]

Here is a question that I came across while doing my problem set questions:

A boat experiences a resistive force that is proportional to v^2. If the maximum speed of a boat is V when one engine is at full throttle, what would be the maximum speed if two engines were used?

I assume this so-called resistive force is like air resistance, but when I searched up the formulas, they're absolutely long and I will never be able to solve those with my current math skills.

The way I tried to see this problem is that if it is related to energy or something, can anyone help me here?

 

[Matterwave]

You need to balance forces. Finding the equation of motion is very difficult because the v^2 term makes the equation of motion a non linear ODE.

 

[PhanthomJay]

The maximum speed implies forces are balanced , with the boat moving at constant velocity, that is, the force delivered by the engine equals the resistive force, kv². Two engines can deliver twice the force. What does this imply about the maximum speed when 2 engines are used? You would need a good knowledge of calculus to find the equation of motion for the speed at any time t, but you don't need any advanced math to solve for the maximum speed.

 

[Solontus]

Edit: nvm, didn't read the post above.