Can the problem about relative motion be solved without using calculus?

[issacnewton]

I have posted the problem and and the solution of part a,b,c in file 1.doc. This is problem
from ch. 4 of serway. It doesn't yet assume calculus. I have question about the part c.
I did it using calculus. but the book's solution uses the kind of arguments which i am not able to understand. Is it possible to solve the part c without using calculus.

thanks

 

[alphysicist]

Hi IssacNewton,

I have posted the problem and and the solution of part a,b,c in file 1.doc. This is problem
from ch. 4 of serway. It doesn't yet assume calculus. I have question about the part c.
I did it using calculus. but the book's solution uses the kind of arguments which i am not able to understand. Is it possible to solve the part c without using calculus.

thanks

Yes, part c can be done without using calculus. Please show your attempt and I or someone else can help you.

 

[issacnewton]

hi al

I think the combined velocity has to make the minimum angle with the direction which is perpendicular to the stream... in that case we can guarantee that the distance traveled downstream will be minimum... but I don't see how to avoid calculus again...

thanks

 

[alphysicist]

hi al

I think the combined velocity has to make the minimum angle with the direction which is perpendicular to the stream... in that case we can guarantee that the distance traveled downstream will be minimum... but I don't see how to avoid calculus again...

thanks

That's right, and another way to say that is that the combined velocity you are looking for is the one that makes a maximum angle away from the stream's flow.

So what are all these possible combined velocities? I would suggest when you draw your vector diagram, draw the stream velocity first, and then think about adding all possible boat velocities (the speed is set, so you can only vary the boat's velocity angle) to that. What do you get?

There are still a few more steps; does that help?

 

[issacnewton]

hi al

yes , basically we have to increase the angle of combined velocity vector with the stream velocity vector... I see what you are saying... now the diagrams given in my attachment are making some sense...so basically we fix the tail of boat velocity vector to the tip of the stream velocity vector and then rotate this boat vector, so that the combined velocity vector makes maximum angle with the stream velocity vector...I see where the argument is going...let me think on these lines...