A person in a canoe can paddle his canoe at a steady 3.6 m/s in still water...

Question

A person in a canoe can paddle his canoe at a steady 3.6 m/s in still water. He wishes to cross a 2.8 km wide river that has a current of 1.6 m/s traveling in the northward direction.

a) If this person first "aims" his canoe straight across the river in the eastern direction, the current will carry him downstream as he paddles across. What will be his actual velocity (magnitude and angle with respect to the eastward direction) as he crosses? How long will it take him to cross the river?

b) If he "aims" the canoe somewhat upstream, he can actually travel straight across the river. In what direction must he aim? What is the actual speed across the river for this situation, and how long will it take him to cross?

Answer 1

I won't solve this for you, but I will give you some hints to point you in the right direction. First draw a figure to show what will be happening.

I'm not sure how realistic this problem is, but you have to assume that the vector components of the velocity act independently, i.e. his eastward velocity is NOT affected by the current. Therefore, his time to cross the river will be 2.8 km divided by his rowing rate, 3.6 m/s. Notice that the units are different and you will have to take that into account.

Once you know his time to cross, you can figure how far down stream the current will take him in that time. This will allow you to calculate the angle at which he ended up from his starting point, using trigonometry.

Then you can figure where he needs to aim upstream