# Two dimensional relative motion; boat and river problem

1. Dec 10, 2012

### physicsstdnt

1. The problem statement, all variables and given/known data
Mary needs to row her boat across a 100-m-wide river that is flowing to the east at a speed of 1.0 m/s. Mary can row with a speed of 2.0 m/s.
a) If Mary points her boat due north, how far from her intended landing spot will she be when she reaches the opposite shore?
b) What is her speed with respect to the shore?

2. Relevant equations
(V_r^2 + V_m^2)^(1/2)
In the y direction (north): d = 2t (where d is distance; t is time)
In the x direction (east): d = 1t

3. The attempt at a solution
a) I solved for t in the y direction and got 50 seconds then i plugged it into the x direction to find out how far off she was from her intended landing spot. The book shows a different answer than what i got.

b) I took the velocity of the river and squared it; then i took the velocity of Mary and squared it; then added and took the square root of the sum. I get 5^(1/2), but the book shows a different answer.

Any help would be appreciated.

2. Dec 10, 2012

### BruceW

Welcome to physicsforums, physicsstdnt (appropriate name, btw). Um, your answers look fine to me (assuming that mary's rowing speed is independent of the speed of the river). What were the book's answers?

3. Dec 11, 2012

### physicsstdnt

The book says that her speed was 3.2 m/s and she landed 300 meters away from her intended landing spot

4. Dec 11, 2012

### BruceW

The book's answer really doesn't make sense to me. It implies that relative to the shore, the boat is moving at roughly 3m/s east and 1m/s north, but since the river is only going at 1m/s east, this would imply she is trying to row downstream, which goes against the whole point of the problem.

It is possible that the book has printed the answer in the wrong place. (or just got the answer wrong). This does happen on occasion.

5. Dec 11, 2012

### D H

Staff Emeritus
The book's answer makes perfect sense if the book solved a slightly different problem than the one stated in the question. The book's answer is for the problem where the river flows at 3 m/s and Mary rows at 1 m/s.

It is also possible that the book's answer is for a question that differs from the question that was asked. This, too, happens on occasion.

6. Dec 11, 2012

### physicsstdnt

Ok. I thought that it might be something like that, but i wanted to be sure. Thanks guys

7. Dec 11, 2012

### BruceW

no problem man. it is annoying when this kind of thing happens

8. Apr 23, 2013

### zakky201

two dimentional problem

Mary rows across a 100m wide river at 2m/s in the northen direction. River flows east at 1m/s. How far from her intended landing spot will she be when she reaches the opposite shore
Any help would be appreciated.[/QUOTE]

9. Apr 23, 2013

### zakky201

Any help would be appreciated.[/QUOTE][/QUOTE]