# Solving for Boat Movement with Vectors: Direction and Speed in a Current

• terainfizik
Keep in mind that the speed of the boat through the water (relative to the water) is not the same as the speed of the boat over the ground (relative to an observer on land). In summary, a boat with a maximum speed of 25 km/hr in still water will move in a direction between North and East when faced with a southeast current of 20 km/hr. The necessary course for the boat to travel North can be determined using vector theory, while the speed of the boat relative to an observer on land can be found using the sine and cosine laws.
terainfizik

## Homework Statement

A boat needs to sail due north , but the current is flowing southeast at a speed of 20km/hr. In still wate, the boat has a maximum speed of25km/hr .

(a) In what direction will the boat actually move (relative to an observer on land)?

(b) What's the course (direction) necessary to that ship could travel North ?

(c) What is the speed of the boat relative to an observer on land?

N/A

## The Attempt at a Solution

(a) North .

(b) East . I using vector theory .

(c) Using theorem phythogoras :

Speed^2 = 25^2 - 20^2
= 225
speed = 15 km/hr

No.

As you know, Pythagoras' theorem only works for right-angled triangles, and you don't have a right-angled triangle here.

You only know two directions and two lengths and the angle between them. That gives you a triangle for (a) and another one for (b).

Draw the triangles (only roughly - I'm not suggesting you measure them!), to make sure you've got them the right way round.

Then use sines or cosines to work out the unknown length and the unknown angle!

Remember that the "sine law" and "cosine law" let you use sine and cosine on non-right triangles. As tiny-tim said, start by drawing a picture and identifying the parts of the triangle.

## 1. How do you solve for boat movement in a current using vectors?

To solve for boat movement in a current using vectors, you will need to break down the boat's velocity into two components: the direction of the boat's movement (represented by a vector) and the speed of the boat's movement (represented by a scalar). Then, you will need to add the current's velocity to the boat's velocity vector to find the overall velocity of the boat in the current.

## 2. What is the importance of taking into account both direction and speed when solving for boat movement in a current?

Taking into account both direction and speed is crucial when solving for boat movement in a current because it allows us to accurately predict the path the boat will take and the time it will take to reach a certain destination. Direction and speed are both essential components of velocity, and considering both factors ensures that our calculations are as precise as possible.

## 3. How do you represent boat movement with vectors?

Boat movement can be represented with vectors by using an arrow to indicate the direction of the boat's movement and the length of the arrow to represent the boat's speed. The direction of the arrow should be in the same direction as the boat's movement, and the length of the arrow should be proportional to the boat's speed.

## 4. What is the difference between velocity and speed when solving for boat movement in a current?

Velocity and speed are often used interchangeably, but they have distinct meanings when solving for boat movement in a current. Velocity is a vector quantity that describes both the direction and speed of an object's movement. On the other hand, speed is a scalar quantity that only describes how fast an object is moving without considering direction.

## 5. How does the current affect the boat's movement in terms of direction and speed?

The current affects the boat's movement in two ways: direction and speed. The direction of the current will determine the direction in which the boat will move, and the speed of the current will influence the boat's overall speed. If the current is in the same direction as the boat's movement, it will increase the boat's speed. However, if the current is in the opposite direction, it will decrease the boat's speed.

• Precalculus Mathematics Homework Help
Replies
9
Views
2K
• Precalculus Mathematics Homework Help
Replies
1
Views
2K
• Precalculus Mathematics Homework Help
Replies
63
Views
5K
• Introductory Physics Homework Help
Replies
11
Views
1K
• Calculus
Replies
6
Views
1K
• Sci-Fi Writing and World Building
Replies
2
Views
442
• Introductory Physics Homework Help
Replies
6
Views
3K
• Engineering and Comp Sci Homework Help
Replies
3
Views
1K
• Introductory Physics Homework Help
Replies
4
Views
2K
• Introductory Physics Homework Help
Replies
7
Views
2K