# Geometric Vectors Homework: River, Motor Boat, Marina

• Macleef
In summary, we have a river that is 2 km wide, flowing at 6 km/h, and a motor boat with a speed of 20 km/h in still water. Using Geometric Vectors, we can determine the following: a) The boat will reach the other bank 0.6 km downstream from the marina. And b) It will take 6 minutes to reach the other bank. The equations used to solve this problem are the sine and cosine laws. The diagram originally drawn is incorrect as the boat will not reach the marina directly across due to the current pushing it down.
Macleef

## Homework Statement

A river is 2 km wide and flows at 6 km/h. A motor boat that has a speed of
20 km/h in still water heads out from one bank perpendicular to the current.
A marina lies directly across the river on the opposite bank. Use Geometric
Vectors to solve this problem.

a. How far downstream from the marina will the boat reach the other bank? (Answer: 0.6 km)
b. How long will it take? (Answer: 6 min)

## Homework Equations

The sine and cosine laws.

## The Attempt at a Solution

Here's what I've done so far, I drew the diagram to the problem. I'm not sure if it's correct or not:

And now, I don't know what to do to answer the questions.

I don't think the diagram is correct. The boat at 20km/h sets out horizontally (perpendicular to the current BUT since the current is pushing it down, the boat gets displaced diagonally. The boat will still reach the other side, but not in a straight line therefore missing the marina. That is why the first question asks how far DOWNSTREAM from the marina does the boat reach the other bank.

## 1. What are geometric vectors?

Geometric vectors are mathematical quantities that have both magnitude and direction. They are represented by an arrow pointing in the direction of the vector and the length of the arrow represents the magnitude or size of the vector.

## 2. How are geometric vectors used in the context of the "River, Motor Boat, Marina" homework problem?

In this homework problem, geometric vectors are used to represent the various forces acting on the motor boat as it travels in the river. These forces include the velocity of the river, the thrust from the boat's motor, and the direction and magnitude of the boat's displacement.

## 3. What is the purpose of using geometric vectors in this homework problem?

The purpose of using geometric vectors is to accurately represent and calculate the different forces and their resultant effect on the motor boat's movement. By using vectors, we can take into account both the magnitude and direction of the forces, which is crucial in solving for the boat's final position.

## 4. How do you represent geometric vectors in mathematical notation?

Geometric vectors are typically represented using boldface letters (e.g. v), with an arrow on top to indicate direction. Another common notation is to represent vectors as column matrices with their x and y components (e.g. v = [vx, vy]).

## 5. What are some real-life applications of geometric vectors?

Geometric vectors have numerous applications in fields such as physics, engineering, and computer graphics. They are used to represent forces in mechanics, current and voltage in electrical circuits, and velocities and accelerations in kinematics. They are also used in computer graphics for 3D modeling and animation.

• Engineering and Comp Sci Homework Help
Replies
3
Views
1K
• Introductory Physics Homework Help
Replies
12
Views
2K
• Introductory Physics Homework Help
Replies
11
Views
2K
• Calculus and Beyond Homework Help
Replies
8
Views
13K
• Introductory Physics Homework Help
Replies
8
Views
1K
• Calculus and Beyond Homework Help
Replies
2
Views
2K
• Introductory Physics Homework Help
Replies
6
Views
3K
• Introductory Physics Homework Help
Replies
3
Views
2K
• Introductory Physics Homework Help
Replies
16
Views
2K
• Calculus and Beyond Homework Help
Replies
8
Views
7K