How Do You Calculate Relative Velocities in One-Dimensional Motion?

[sebmista]

Ok I just can't figure this one out. And my book doesn help at all since all the examples give you the x and y components. This problem doesn't have but one.

Two canoeists in identical canoes exert the same effort paddling and hence maintain the same speed relative to the water. One paddles directly upstream (and moves upstream), whereas the other paddles directly downstream. With downstream as the positive direction, an observer on shore determines the velocities of the two canoes to be -1.2 m/s and +2.9 m/s, respectively.

(a) What is the speed of the water relative to shore?
m/s
(b) What is the speed of each canoe relative to the water?
canoe going upstream m/s
canoe going downstream m/s

How do I even begin?

 

[tony873004]

Draw a diagram, make some triangles and do some trig. You'll have x and y coordinates in this too.

 

[steve23063]

Hints:
1. Draw a diagram showing the canoes and which way they are moving
2. Think in terms of vectors because you need to add velocities in this problem
3. Why are you adding velocities? Well one of the canoes is flowing downstream at 2.9m/s. This isn't just because the person in the canoe is rowing really fast. It's also because the water is flowing downstream. So

total velocity of one of the canoes (relative to the shore) = 2.9m/s = velocity of water + velocity of canoe due to rowing

4. Make sure you understand what "relative to the shore" means. 2.9m/s is how fast the canoe would pass you if you were just standing on the shore. If you were just floating in the water as it carried you downstream, the canoe would still pass you because the person inside is rowing but it would pass you at a slower velocity. This slower velocity is the velocity of the canoe "relative to the water".


edit: Tony, there is no need for x and y coordinates in this problem. The canoes are flowing directly with or against the water. There's no sideways movement...just need one coordinate which you can call x or y