You row a boat, click for picture, perpendicular to the shore of a river that flows at 3.0 m/s. The velocity..

Question

You row a boat, click for picture, perpendicular to the shore of a river that flows at 3.0 m/s. The velocity of your boat is 4.0 m/s relative to the water.

a. What is the velocity of your boat relative to the shore?

b. What is the component of your velocity parallel to the shore? Perpendicular to it?

Please help me with this problem.
I'm having trouble understanding it.

I forgot to add a picture link.

*Picture link:
http://img208.imageshack.us/img208/7021/scanye9.jpg

Answer 1

a) We have two velocities that act as a triangle. We have 3 m/s and 4 m/s using pythagoreans to get the hypotnuse we see the standard 3 4 5 type triangle 3^2 + 4^2 = Z^2

(9 + 16) ^ .5 = 5 m/s

It's not specified whether or not 'relative to the shore' is a point on the shore or the shore in general.

Point on the shore = 5 m/s
Shore in general = 4 m/s

b) parallel to the shore you are 3 m/s
perpindicluar to the shore you are 4 m /s

b) Parallel component is 3 m/s + 3 m/s = 6 m/s
perpindicular component is 2.64 m/s


(the problem would have been more involved if it stated that your boat REMAINED perpendicular to the shore)

Answer 2

I'll answer part b. first: the component of your velocity parallel to the shore is 3.0 m/s. Perpendicular to it: 4.0 m/s. This is because your rowing of the boat is independent of the river's flow (and vice versa) so the values stated in the problem are the exact answers. As to part a., it depends on a more precise definition of "relative to the shore." If by that any part of the shore is meant, or to put it another way, if it means "the shore" as a concept, not an exact point on the shore, then your velocity along it and toward it are the answers to part b. Since that is a bit silly, it seems likely the problem wants you to think of an exact point on that shore and figure the velocity relative to that point. If you pick as that point the spot that you will first touch shore while rowing from where you are now at 4.0 m/s in water flowing at 3.0 m/s then you have a very nice triangle you may picture to better grasp the answer. Using the Pythagorean formula, you find your velocity relative to that exact point is 5.0 m/s. I know this seems exceedingly strange since, if the water were not flowing, you could row to a closer place on the shore in the same time at only 4.0 m/s but remember that it still takes exactly the same time and the flow of the river water makes you actually go farther during that same time so it really does make sense for the answer to be higher than either of the velocities you already know.

Answer 3

a. The river's current is downstream. The boat's velocity is across the river, perpendicular to the current. The resultant velocity is the hypotenuse. The known sides are 3 and 4 so the 3rd side is 5 units. The velocity of your boat relative to the shore = 5 m/s.

b. Velocity parallel to the shore is the river's velocity = 3 m/s.
Perpendicular to the shore is the boat's speed thru the water = 4 m/s.

Answer 4

tricky issue. check out on a search engine. it can assist!