The Motor Boat

Work=force*distance!

 

Log in or Sign up to hide all adverts.

All measures of the boat are relative to the embankment because that is what was measured in still water! The embankment is at a zero velocity!

 

Log in or Sign up to hide all adverts.

No, the prop is turning at the same rate regardless of the current, so the RPM remains constant. This problem does not involve loading, so that's not a concern.
Yes, you can't give it more throttle, which is why the speed changes relative to shore.

 

Log in or Sign up to hide all adverts.

The "loading" is a hidden concept in this scenario, because the "still water" time was 1.25 hours, whereas the "loaded" (upstream) and "unloaded" (downstream) times were different than in still water.

 

And the current is moving relative to the bank. The boat is moving in coordinates relative to the bank, but not physically. It's not clawing the bank. It's pushing water molecules. Physically, then, the boat is moving relative to the water. When the boat enters the 3.27 km/hr current, it slows relative to the bank - to a speed of 4.73 km/hr, but continues at 8 km/hr relative to the water. After 5 km, it turns around, still moving at 8 km/hr relative to the stream, but gaining 3.27 km/hr from the current, now moving at 11.27 km relative to the bank.

 

No loading would require us to have data not provided so we ignore loading in the problem. This is a simple problem in Galilean relativity, nothing more.

 

The movement of the boat is measured compared to the embankment, not the water. The water could have traveled 100 MPH when the boat was traveling upstream in current, or the water could have been traveling 10 MPH while the boat was traveling upstream! You have no idea how fast the current was flowing compared to the embankment!

 

Motor Daddy, any analogy you draw between the boat and a car will be flawed, because cars travel on stationary roads, while the boat is traveling on flowing water. I'll refer to the road and the water as the "substrates" of motion for the car and boat, respectively. In both cases, as long as we neglect air resistance, the vehicle only interacts with the substrate, so its velocity relative to the substrate is the only thing that can affect how it behaves. In a car, the horsepower it takes to go faster depends only on how fast you're going relative to the road. In a boat, the load on the crank depends only on how fast you're going relative to the water.

This means that the speed of a vehicle relative to its substrate is entirely independent of the substrate's own movement, so it is correct to say that the total velocity of a vehicle is equal to its velocity on a still substrate plus the velocity of the substrate. This means that the boat is putting out the same engine power and moving at the same speed relative to the water going both ways, but the additional motion of the water itself changes the speed of the boat relative to the shore. In the case of the car on a highway, the velocity of the substrate is zero, so you can't observe this effect. If we use Aqueous Id's clever suggestion of driving around on an aircraft carrier, we could make the car on a moving road move identically to the boat in moving water.

 

In this scenario the measurements were conducted according to the embankment, not the substrate!

 

The 8 km movement of the boat is referenced to still water which tells us that as long as the water is not moving, the speed relative to the bank is 8 km/hr.

When the water moves relative to the bank, it carries the boat with it. Thus, with no power, the boat will move relative to the bank, at the speed of the current. In the original statement of the problem we knew the current was moving at 3 km/hr, which gave a distance in each leg of 5.15625 km + 5.15625 km = 10.3125 km total distance traveled (post #10). This version of the problem changed that to 5 km/hr, increasing the current to 3.27 km/hr (post #13).

 

No information is given to make any determination of loading. It's not germane.

 

Are you saying that if the water moves at 10km/hr compared to the embankment that the boat is traveling with the water at 10km/hr in the same direction as the water compared to the embankment?

 

Assume they kill the engine and drift back. How much work is done?

 

That's true, but we also know that the boat doesn't interact with the embankment. The fact that the vehicle only interacts with the substrate has nothing to do with how we took our measurements; it's a simple fact of how boats work. So before we even look at the boat, we can confidently say that its maximum speed relative to the water does not depend on the speed of the water itself. Once we know that, we can measure the boat's max speed in still water with buoys if you're really that bothered by the clocks on the embankment.

 

Yes. This is correct. (As long as the boat is idling.)

 

Force times distance! If a boat is floating in current water with no engine running, the water is doing work equal to the force times the distance.

 

Speed of the boat relative to the bank = speed of the water relative to the bank + speed of the boat relative to the water

 

The max speed of the boat in water is unknowable unless you test it! You can claim that a 1,000 HP boat will travel 100 MPH in 100 MPH current, but until you MEASURE it you are just blowing smoke, and I can guarantee you your math answer is DIFFERENT than the actual measured speed!

 

Try again! The boat's speed is not relative to the water, it's relative to the embankment. The boat's speed relative to the water is called closing speed.

 

The boat speed is relative to both.

In this problem the boat speed is relative to the water and the water speed is relative to the bank. As long at the water is still, the boat speed relative to the water = the boat speed relative to the bank. But when the boat enters a current, that scenario changes. Now the speed relative to the water is still 8 km/hr but the boat speed relative to the bank is -3.27 km/hr ± 8 km/hr , depending on the direction of the boat.