How Does River Flow Impact Boat Speed Calculations?

[BrownBoi7]

A_________________________
-
-
W=45m - <------- Flow of the water
-
-
__-_______________________B

A boat is to travel from position B to position A in 62 seconds as identified on the diagram above. Let the river width W and horizontal length L be defined as follows:
W= 45 m and L = 184 m. The river flows at 1.6m/s to the left as shown in the diagram above.
1. How fast and in what direction must you paddle a boat to reach point A?
2. How fast must you paddle for the return trip along the same path to take the same amount of time?

 

[jackarms]

Welcome to Physics forums! To start off, what are your initial thoughts for how to solve this? What have you attempted so far?

 

[BrownBoi7]

Thank you jackarms.
I have been stuck on this for some time now. In my defense, I missed two consecutive lectures when 1D and 2D was covered. Hehe. From what I have read since this morning, I'll try to answer it:

(1) Two parts:
Direction: The boat will have to go opposite to the river current so the velocities cancel the the boat goes up to the North (Point A) I'm unsure of the angle I need to calculate on this one.
Fast: Equal velocity to the river current?

(2) Get the time taken from (1). Treat it as a triangle and find the hypotenuse (AB)
AC= 45m
CB= 184 m
Therefore, AB= sqrt(45)^2+(184)^2
AB= 189.42 m
Speed= Distance x Time
189.42xT

Am I on a right track here?

 

[jackarms]

You are: the only problem you'll run into is that the problem involves speed both down the river and across it, so it will be pretty difficult to combine those into one speed to find the time. Basically it's just because if you're going across the hypotenuse of a triangle like you said, you'll have the speed of the boat influenced in the direction of the river, but not perpendicular to it.

I think a good way to go about this would be to split up the speed into components -- so you have one component of the boat's speed (call it y) that goes across the river, and another component (call it x) that goes in the direction of the river. This way you can split up the 2D problem into 2 1D problems -- one that goes directly along the river the horizontal distance, and another that goes across the river the vertical distance. Then as long as you mandate that the time to cover the respective distances of the components be the same, you can solve for both components, and thus the direction, total speed, etc.

 

[HalfLostAndSearching]

1. To reach point A in 62 seconds, the boat must travel a horizontal distance of 184 meters. Since the river is flowing at 1.6 m/s to the left, the boat must paddle at a speed of 2.97 m/s to the right to counteract the flow of the water and reach point A in the given time frame.

2. For the return trip, the boat must travel a horizontal distance of 184 meters in 62 seconds. Since the river is flowing at 1.6 m/s to the left, the boat must paddle at a speed of 0.03 m/s to the left to counteract the flow of the water and reach point B in the given time frame. This is because the total distance traveled by the boat is the same, but the boat is now moving in the opposite direction of the river's flow.