# Relative Velocity

1. Feb 3, 2010

### casemeister06

1. The problem statement, all variables and given/known data

Two piers, A and B are located on a river: B is 1500 m downstream from A. Two friends must make round trips from pier A to B and back. One rows a boat at a constant speed of 4 km/hr relative to the water; the other walks on the shore at a constant speed of 4 km/hr. The velocity of the river is 2.80 km/hr in the direction from A to B. How much time does it take each person to make the round trip.

2. Relevant equations

Vavg = $$\Delta x / \Delta t$$

VP/A = VP/B + VB/A

3. The attempt at a solution

I'm assuming we would have to find a single average velocity for both the boat and the person then take each velocity and let it be the dividend of the total distance to solve for the time. The person is relatively easy to solve for. For the boat though. I'm having trouble setting up the relative velocity equation. I get confused on what my point of reference should be and if the speeds are with respect to the water or the earth.

2. Feb 3, 2010

### casemeister06

Sorry about the double post. Computer lagged out.

3. Feb 3, 2010

### ByronT

First, make sure you convert km/hr to m/s.

4 km/hr = ~ 1.1 m/s
2.8 km/hr = ~ .78 m/s

We know that friend 1 is going to travel fast from A to B on the first part of the trip because he has a current behind him. His velocity of rowing will just be added with the velocity of the water. When he rows back, he'll be working against the current, so we will subtract the water's speed from his rowing speed, and he'll move more slowly.

It might be easier for you to think in terms of splitting the problem up. They go from A to B at a certain speed, and it takes them a certain time. Then, they go from B to A at a certain speed, and it takes the boater longer than his first part of the trip, since he's rowing against a current rather than with it. The other friend walks the same speed the whole time.

Use the equation time = distance/velocity. For each person, add their times for each part of the trip.

It doesn't make sense to find the average velocity for the boater because you don't know how long he's rowing downstream and upstream. It's obviously easy finding the average velocity for the walker, though.

The speeds are with respect to an observer on the earth. It wouldn't make sense for the problem to give you the speed of the water with respect to the moving water. Don't try to think too deeply about problems like these. The important thing is to break them up into multiple problems if you are having trouble understanding.

Last edited: Feb 3, 2010
4. Feb 3, 2010

### casemeister06

Thanks for the help. I guess I was thinking way to hard.