Problem in Great Courses Video On Physics

[Joa Boaz]

[ mod note: moved from general physics so homework template is missing ]

At the end of each lesson, the lecturer gives a problem. The question is: A rectangular, flat-bottomed rowboat has a mass of 120 kg when empty. It's 3 meters long, 1 meter wide, and 0.24 meters deep. How many 85 kg people could it hold before swamping?

My answer was 7, but apparently according to the video the answer is 6. In addition, he gives a final answer of 590 kg without including the boat weight. But if I multiply 6*85, it does not equal 590. So, I am really confused since he merely provides the final answer of 6 people. Can anyone help?

Thank you.

 

[Merlin3189]

I can't see anything that you've got wrong. On the other hand, I can't really see what you've done at all, except your answers. Perhaps it is generally a good idea to explain yourself it bit more - show your calculations.
As it stands, I think you are correct, so I'd want to see the actual question, to check that you've not missed any details.

Edit: BTW in real life, loading a boat to the gunnels is not a good idea. It would certainly get swamped. Perhaps he allowed a few mm of freeboard.

 

[Joa Boaz]

Basically, my equation was as followed:
(density of water)*(length*width*depth of the boat measurement) = (weight of the boat + weight of all the people on the boat)

(1000 kg/m³)*(3 m * 1 m * 0.24 m) = 720 kg

720 kg - 120 kg (the weight of the boat) = 600 kg

600 kg / 85 kg = 7.05

Thus, the final answer seems to be about 7 people.

 

[Merlin3189]

Yes, exactly what I thought.
As I said, I can only wonder whether there was some other detail in the question, for example suggesting that some of the boat should be above the water.
7 people is 695 kg, leaving 5kg of reserve buoyancy - equivalent to about 1.7mm of freeboard.
6 people is 510 kg, leaving 90kg reserve buoyancy, equivalent to 3cm of freeboard. That is better, but would hardly meet Board of Trade standards.
Incidentally, in the EU a standard person is 75kg rather than 85kg. Since I'm 90kg, I think the 85kg is more realistic!
Unless the Q has specified some further details, I would say you were correct.