# Simple boat and river question(Vectors)

• dmitrip
In summary, Pierre is rowing his boat across a river at a speed of 10 km/h while the river is flowing at 6 km/h. To travel directly across the river, he needs to row at an angle relative to the shore, which can be calculated using the equation Vbg = Vbw + Vwg.
dmitrip

## Homework Statement

In his rowboat, Pierre heads directly across a river at a speed of 10 km/h. The river is 120m wide and is flowing at 6 km/h.

Suppose Pierre wants to row directly across the river. At what angle relative to the shore should he head?

I would really appreciate help with this question, since I know that it is suppose to be straight forward and for some reason I just can't solve it! must be because I didn't have much of a sleep.

thanks alot

Vbg = Vbw + Vwg
where Vbg is the velocity of the boat relative to the ground, Vbw is the velocity of boat relative to water, Vwg is the veloctiy of the water relative to the ground.

To solve this problem, we need to use vector addition to determine the direction that Pierre should row in. The velocity of the river can be represented by a vector pointing to the right with a magnitude of 6 km/h. The velocity of the boat can be represented by a vector pointing directly across the river with a magnitude of 10 km/h.

To find the angle between these two vectors, we can use the tangent function. The formula for tangent is opposite/adjacent, which in this case would be the y-component of the velocity of the boat (10 km/h) divided by the x-component of the velocity of the river (6 km/h).

Therefore, the angle that Pierre should row at can be calculated as arctan(10/6) = 59.04 degrees. This means that he should row at an angle of approximately 59 degrees relative to the shore.

I hope this helps you solve the problem. It is important to get enough rest before attempting difficult problems, as a well-rested mind can think more clearly and effectively. Keep practicing and you will get better at solving these types of questions. Good luck!

## 1. What is a vector?

A vector is a quantity that has both magnitude (size or length) and direction. It is often represented graphically as an arrow, with the length of the arrow representing the magnitude and the direction of the arrow representing the direction of the vector.

## 2. How is a vector different from a scalar?

A scalar is a quantity that only has magnitude, while a vector has both magnitude and direction. Examples of scalars include temperature, mass, and time, while examples of vectors include velocity, force, and displacement.

## 3. How do vectors apply to boats and rivers?

In the context of boats and rivers, vectors are used to represent the velocity of the boat and the velocity of the river. The direction and magnitude of these vectors can be used to determine the overall velocity of the boat relative to the river.

## 4. How do you calculate the overall velocity of a boat on a river using vectors?

To calculate the overall velocity of a boat on a river, you can use vector addition. This involves adding the velocity vectors of the boat and the river together to find the resultant vector, which represents the overall velocity of the boat relative to the river.

## 5. Why is understanding vectors important in studying boats and rivers?

Understanding vectors is important in studying boats and rivers because it allows us to accurately describe and predict the movement of the boat on the river. By using vectors, we can account for the direction and magnitude of the boat's velocity and how it is affected by the velocity of the river.

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