# Relative Velocity Homework: Boat & Person Round Trip Time

• casemeister06
In summary, it takes friend 1 about twice as long to make the round trip as friend 2 does, even though friend 2 is moving at the same speed.
casemeister06

## Homework Statement

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.

## Homework Equations

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

VP/A = VP/B + VB/A

## 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.

Sorry about the double post. Computer lagged out.

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

## 1. What is relative velocity?

Relative velocity is the velocity of an object with respect to another object. It takes into account the motion of both objects and is typically measured in meters per second (m/s).

## 2. How does relative velocity apply to a boat and a person?

In the context of a boat and a person, relative velocity refers to the motion of the person as observed from the boat and vice versa. This is important when considering the round trip time for a boat and person to travel a certain distance.

## 3. How do you calculate relative velocity?

The formula for relative velocity is V_AB = V_A - V_B, where V_AB is the relative velocity of object A with respect to object B, V_A is the velocity of object A, and V_B is the velocity of object B. Alternatively, you can use the Pythagorean theorem to calculate relative velocity if the velocities are not in the same direction.

## 4. What factors can affect the relative velocity of a boat and a person?

The relative velocity of a boat and a person can be affected by the direction and speed of the wind, the current of the water, and any obstacles in the water. It can also be influenced by the velocity of the boat and the person relative to the shore or other fixed point.

## 5. How can relative velocity be useful in solving problems involving a boat and a person's round trip time?

Relative velocity is essential in solving problems involving a boat and a person's round trip time because it allows us to compare the velocities of the boat and the person relative to each other. By considering their relative velocities, we can determine the total distance traveled and the total time taken for the round trip.

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