# Relative Motion - River/Boat problem

• Kosmos77
In summary, the boat takes 2.80 hours to travel 30.0 km down a river and 4.50 hours to return. To find the speed of the river, we need to set up two equations and use the fact that the distance traveled in both cases is the same. This allows us to find a relationship between the boat speed and the current speed, which we can then use to solve for the current speed.
Kosmos77

## Homework Statement

A boat takes 2.80 hours to travel 30.0 km down a river, then 4.50 hours to return. How fast is the river flowing

Vac = Vab + Vbc

## The Attempt at a Solution

I wasn't quite sure how to use the formula that the professor gave us which is above for this particular problem. The way I see it, since the problem doesn't say their is a change in acceleration, I'm thinking the speed of the boat IS the speed of the river seeing as it is saying "down" a river... so I just took 30 / 2.8 which gives me the speed of the boat but... It's not the answer.

There are a couple of steps involved here:

1. Set up two equations for the speed of the boat when it is going with and against the current.

2. Set up an equation in which you state that the distance traveled in both cases in exactly the same.

3. Find a relationship between the boat speed and the current speed using the above.

4. Use the fact that they give you the distance traveled to your advantage. With this, you can set up another equation relating the boat and current speed. With two equations and two unknowns, you can finish the problem.

I would approach this problem by first defining the variables and their relationships. In this case, we have the distance traveled (30.0 km), the time taken to travel that distance (2.80 hours), and the speed of the boat (which we can calculate by dividing the distance by the time, giving us 10.71 km/h). We also have the return trip, which takes 4.50 hours.

Using the formula Vac = Vab + Vbc, we can determine the speed of the river by subtracting the speed of the boat from the total speed of the boat and river. In this case, since we are given the time and distance for the return trip, we can calculate the total speed of the boat and river (30 km/4.5 hours = 6.67 km/h). Subtracting the speed of the boat (10.71 km/h) from this total gives us a speed of 6.67 km/h for the river.

Therefore, the river is flowing at a speed of 6.67 km/h. This approach allows us to use the given information to solve for the unknown variable in a systematic and scientific manner.

## What is relative motion?

Relative motion refers to the movement of an object in relation to another moving object.

## How does relative motion apply to a river/boat problem?

In a river/boat problem, relative motion is used to determine the speed and direction of a boat in a river, taking into account the flow of the river.

## What are the key factors to consider in a river/boat problem?

The key factors to consider are the speed of the boat, the speed of the river, and the angle at which the boat is traveling in relation to the direction of the river's flow.

## What is the equation used to solve a river/boat problem?

The equation used is: Boat's speed = River's speed + (sinθ) x (River's speed).

## Can relative motion be applied to other scenarios besides a river/boat problem?

Yes, relative motion can be applied to any scenario where two objects are in motion and their movements are interrelated.

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