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Here is a sample question i got for homework:

A river ﬂows due east at 2.32 m/s. A boat

crosses the river from the south shore to the

north shore by maintaining a constant velocity of 13.5 m/s due north relative to the water.

If the river is 322 m wide, how far downstream is the boat when it reaches the north

shore? How many degrees oﬀ course is the boat

forced by the current?

Answer in units of ◦

Using Trig my (correct) answer is 13.69789765 m and 9.7511 degrees.

Is there a way I could have found one of these answers using vector calculus? I don't care how unnecessarily complex it is, its fun!

P.S. i am familiar with line integrals so that won't be a problem

Thanks!