Finding the Correct Way to Cross a River in a Canoe

[r.meghdies]

I have a test on Friday on this...now my textbook, 2 physics teachers and other people say I'm wrong but i know i still think I'm right. what is the right way to answer this i explained option 2 is correct. please give explanation of why, or examples i can use to prove it.

Thank you!

A canoeist who can paddle 5km/h in still water wishes to cross a 400 m wide river, with 2km/h current. If he steers the canoe perpendicular to the current and wants to get straight across the river how long will it take him to cross the river.

Which way is right? and why?

hypotenuse = 5 km/h
...| (ignore dots)
...| < 2 km/h
__________|
^ 400 m & 4.58 km/h
Θ = 22*

option 1:

t = 0.4 km / 4.58 km/h


option 2:
cosΘ = a / h
cos 22 = 0.4 km / h
h = 0.43 km

now i do t= .43km / 4.58 km/h

t= 5.63 minutes

 

[JaWiB]

You could find the component of his velocity perpendicular to the current as \sqrt{5^{2}-2^{2}} then divide .4 by that. No sines or cosines necessary.

Edit: Actually, I'm not sure how this makes sense. It says the canoeist is paddling perpendicular to the current, but he can't do that and make it straight to the other shore unless the current is also pointed toward the shore.