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.

 

[rwisz]

I can provide a response to this question by explaining the concept of resistive force and its relationship to the maximum speed of a boat.

First, let's define what resistive force is. Resistive force is any force that opposes the motion of an object. In the case of a boat, this could be forces such as air resistance, water resistance, and friction.

In this scenario, the resistive force is proportional to the square of the boat's velocity (v^2). This means that as the boat's speed increases, the resistive force also increases. This is because at higher speeds, the boat is pushing against more air and water molecules, resulting in a greater resistance.

Now, let's consider the scenario of a boat with one engine at full throttle. In this case, the boat is able to reach a maximum speed of V. This means that at this speed, the force generated by the engine is equal to the resistive force acting on the boat.

If we were to add a second engine, the combined force generated by the two engines would be greater than the resistive force. This would result in the boat being able to achieve a higher maximum speed than V.

The exact maximum speed with two engines would depend on the power and efficiency of the engines, as well as the design of the boat. However, we can say that it would be proportional to v^2, just like the resistive force. This means that the maximum speed with two engines would be greater than V, but not necessarily twice as fast.

In conclusion, adding a second engine to a boat would increase its maximum speed, but the exact increase would depend on various factors. The relationship between the maximum speed and the resistive force is proportional to v^2, meaning that the resistive force will always limit the maximum speed that can be achieved.