# Solving Relative Velocity River Crossing Problem

• megkirch
In summary, the problem involves a person crossing a river with a rowboat and trying to determine how far downstream they reach the opposite shore. The river has a velocity of 4.043 km/hr and the person rows with a maximum velocity of 3.138 km/hr relative to the water. Using the equations VAC=VAB+VBC and Vbg=Vbw+Vwg, the person tries to calculate the distance downstream by dividing the width of the river by the velocity of the boat and multiplying by 60. However, this approach is incorrect as it results in a speed instead of a distance and does not account for the units. A new approach is needed to solve the problem.
megkirch

## Homework Statement

A person in a rowboat crosses a river which flows with 4.043 km/hr. The person rows with maximum velocity of 3.138 km/hr relative to the water (measured while rowing on a still lake) and heads the boat straight across the river - along a line at 90 degrees with respect to the river shore pointing to a point on the opposite shore. How far downstream from this point in km does the person reach the opposite shore if the river is 0.2773 km wide.

## Homework Equations

VAC=VAB+VBC, then
Vbg=Vbw+Vwg

## The Attempt at a Solution

I tried tan-1 (4.043/3.138)= 52.2 as theta
3.138(cos)(52.2)=1.92
then i thought i have to divide the width. (.2773/1.92)=.1444
but that's wrong, i tried this problem over and over again and i just don't know what I am doing wrong.

megkirch said:

## Homework Statement

A person in a rowboat crosses a river which flows with 4.043 km/hr. The person rows with maximum velocity of 3.138 km/hr relative to the water (measured while rowing on a still lake) and heads the boat straight across the river - along a line at 90 degrees with respect to the river shore pointing to a point on the opposite shore. How far downstream from this point in km does the person reach the opposite shore if the river is 0.2773 km wide.

## Homework Equations

VAC=VAB+VBC, then
Vbg=Vbw+Vwg

## The Attempt at a Solution

I tried tan-1 (4.043/3.138)= 52.2 as theta
3.138(cos)(52.2)=1.92
then i thought i have to divide the width. (.2773/1.92)=.1444
but that's wrong, i tried this problem over and over again and i just don't know what I am doing wrong.
Can you explain why you did what you did in your solution? You should have a good reason for each step.

Here are some questions to consider:

What are the units of 1.92? Do they match what you think it's supposed to represent?

What are the units of your final answer? Are they consistent with what you're trying to find?

Would you mind posting a diagram of what you did. The diagram is very important

Im trying to follow the notes from my professsor that i have for a similar problem. I set up a triangle and got opposite over adjacent that's why i used tan-1.
1.92km/h , after i divided out the width I multiplied .1444 by 60 because its km/hour and got 8.7 km/h. That answer is still wrong. I am not sure what else to try.

I don't know how to post a diagram on this. I have a right triangle. with bw=3.138 on the y axis, and wg= 4.043 on the x axis, with bg that I am trying to find on the hypotenuse.

Don't try to work it out using your diagram. I find that for this type of Relative Velocity question you just use it as a visualisation aid. It sets up the maths, and the solving tends to be 100% maths.

Try this, I hope you're familiar with i and j notation.

River Velocity... Vr = 4.043i + 0j
ACTUAL Boat Velocity... Vb = XcosA i + XsinA j
Boat relative to river... Vbr = 0i + 3.138j

Do you understand this? Can you figure out the rest?

Im sorry, I am not familiar with the i and j notation.

i axis = x-axis
j axis = y axis

Basically the same co-ordinate system just different letters

megkirch said:
Im trying to follow the notes from my professsor that i have for a similar problem. I set up a triangle and got opposite over adjacent that's why i used tan-1.
1.92km/h , after i divided out the width I multiplied .1444 by 60 because its km/hour and got 8.7 km/h. That answer is still wrong. I am not sure what else to try.
That answer is a speed or velocity, right? The units are length per time. But you're looking for how far downstream the boat goes. You're looking for a distance or displacement, which has units of length. Another problem is that your final answer doesn't actually have units of km/h. You had km/h but then divided the width, which has units of km, by it, so your answer should have units of km/(km/h) = h.

You need a completely new approach to solving the problem. Start by figuring out how long it takes the boat to cross the river.

## 1. What is the relative velocity river crossing problem?

The relative velocity river crossing problem is a physics problem that involves determining the speed and direction of an object's motion in relation to another object or observer. In this scenario, the object is moving across a river or body of water, and the problem requires calculating its velocity relative to the water and the riverbank.

## 2. How do you solve the relative velocity river crossing problem?

To solve the relative velocity river crossing problem, you must first understand the concept of relative velocity and how it is affected by the motion of the object and the river. Then, you can use vector addition and trigonometry to calculate the object's velocity relative to the water and the riverbank.

## 3. What are the key variables in the relative velocity river crossing problem?

The key variables in the relative velocity river crossing problem are the speed of the object, the speed of the river's current, and the angle at which the object is moving relative to the river's direction. These variables are used to calculate the object's velocity relative to the water and the riverbank.

## 4. What are some common mistakes when solving the relative velocity river crossing problem?

One common mistake when solving the relative velocity river crossing problem is forgetting to account for the angle at which the object is moving in relation to the river's direction. Another mistake is using the object's velocity relative to the riverbank instead of its velocity relative to the water.

## 5. How is the relative velocity river crossing problem used in real life?

The relative velocity river crossing problem is used in real life scenarios such as navigation, boat trips, and water sports. It is also applicable in understanding the motion of objects in a moving medium, such as airplanes flying in the wind or cars driving through a current of air.

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