The Jolly Jack Sailed For 10 Km On A Course Of 060°, And Then Sailed For 10 Km On A Course Of 180°.a. Make A Scale Drawing Of The Boat's Course So Far, Taking 1 Cm To Represent 1 Km.b. What Is The Boat's Distance And Bearing From The Starting

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Introduction

In this problem, we are tasked with creating a scale drawing of the Jolly Jack's course and determining its distance and bearing from the starting point. The Jolly Jack sailed for 10 km on a course of 060°, and then sailed for 10 km on a course of 180°. To solve this problem, we will use basic navigation concepts and geometric principles.

Step 1: Understanding the Course

The Jolly Jack's course consists of two segments:

  • The first segment is a 10 km sail on a course of 060°. This means the boat sailed 10 km east.
  • The second segment is a 10 km sail on a course of 180°. This means the boat sailed 10 km west.

Step 2: Creating a Scale Drawing

To create a scale drawing, we will use a scale of 1 cm to represent 1 km. This means that every 1 cm on the drawing represents 1 km in real life.

Scale Drawing

Here is a scale drawing of the Jolly Jack's course:

  +---------------------------------------+
  |                                             |
  |  10 km east (060°)                      |
  |                                             |
  |  +---------------------------------------+
  |  |                                         |
  |  |  10 km west (180°)                    |
  |  |                                         |
  |  +---------------------------------------+
  |                                             |
  |  Starting point (0, 0)                  |
  |                                             |
  +---------------------------------------+

Step 3: Determining the Distance and Bearing

To determine the distance and bearing from the starting point, we need to find the final position of the Jolly Jack.

Since the Jolly Jack sailed 10 km east and then 10 km west, the net displacement is 0 km. This means the Jolly Jack is back at the starting point.

However, we need to consider the bearing. The Jolly Jack sailed 10 km east and then 10 km west, which means it is now 10 km west of the starting point.

Distance and Bearing

The distance from the starting point is 10 km.

The bearing from the starting point is 270° (or west).

Conclusion

In this problem, we created a scale drawing of the Jolly Jack's course and determined its distance and bearing from the starting point. The Jolly Jack sailed 10 km east and then 10 km west, resulting in a net displacement of 0 km. However, the bearing is 270° (or west), indicating that the Jolly Jack is 10 km west of the starting point.

Mathematical Formulation

Let's denote the starting point as (0, 0) and the final position as (x, y).

The Jolly Jack sailed 10 km east, which means the x-coordinate increases by 10 km.

The Jolly Jack sailed 10 km west, which means the x-coordinate decreases by 10 km.

The net displacement is 0 km, which means the x-coordinate remains the same.

The bearing is 270° (or west), which means the y-coordinate is -10 km.

Therefore, the final position is (0, -10).

Mathematical Formulation (continued)

We can use the Pythagorean theorem to find the distance:

distance = √(x² + y²) = √(0² + (-10)²) = √(100) = 10 km

The distance from the starting point is 10 km.

The bearing from the starting point is 270° (or west).

Conclusion (continued)

In this problem, we used basic navigation concepts and geometric principles to create a scale drawing of the Jolly Jack's course and determine its distance and bearing from the starting point. The Jolly Jack sailed 10 km east and then 10 km west, resulting in a net displacement of 0 km. However, the bearing is 270° (or west), indicating that the Jolly Jack is 10 km west of the starting point.

Final Answer

The final answer is:

  • Distance: 10 km
  • Bearing: 270° (or west)

Discussion

This problem requires a basic understanding of navigation concepts and geometric principles. The Jolly Jack's course consists of two segments, and we need to find the final position by considering the net displacement and bearing.

The scale drawing is a useful tool for visualizing the course and determining the distance and bearing. The Pythagorean theorem is used to find the distance, and the bearing is determined by considering the direction of the final position.

Q: What is the Jolly Jack's course?

A: The Jolly Jack's course consists of two segments: a 10 km sail on a course of 060° (east) and a 10 km sail on a course of 180° (west).

Q: What is the net displacement of the Jolly Jack?

A: The net displacement of the Jolly Jack is 0 km, since it sailed 10 km east and then 10 km west.

Q: What is the bearing of the Jolly Jack from the starting point?

A: The bearing of the Jolly Jack from the starting point is 270° (or west), since it is 10 km west of the starting point.

Q: How can we determine the distance and bearing of the Jolly Jack?

A: We can determine the distance and bearing of the Jolly Jack by creating a scale drawing of its course and using the Pythagorean theorem to find the distance.

Q: What is the scale of the scale drawing?

A: The scale of the scale drawing is 1 cm to represent 1 km.

Q: How can we use the Pythagorean theorem to find the distance?

A: We can use the Pythagorean theorem to find the distance by considering the net displacement and bearing of the Jolly Jack. The Pythagorean theorem states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Q: What is the final position of the Jolly Jack?

A: The final position of the Jolly Jack is (0, -10), since it is 10 km west of the starting point.

Q: How can we use the final position to determine the distance and bearing?

A: We can use the final position to determine the distance and bearing by considering the x and y coordinates. The distance is the square root of the sum of the squares of the x and y coordinates, and the bearing is the direction of the final position.

Q: What is the distance from the starting point to the final position?

A: The distance from the starting point to the final position is 10 km.

Q: What is the bearing from the starting point to the final position?

A: The bearing from the starting point to the final position is 270° (or west).

Q: What is the significance of the Jolly Jack's course?

A: The Jolly Jack's course is a classic example of a navigation problem, and it requires a basic understanding of navigation concepts and geometric principles. The course demonstrates how to use the Pythagorean theorem to find the distance and bearing of a point.

Q: How can we apply the concepts learned from the Jolly Jack's course to real-world navigation?

A: We can apply the concepts learned from the Jolly Jack's course to real-world navigation by using the Pythagorean theorem to find distances and bearings, and by creating scale drawings to visualize courses and positions.

Conclusion

In this Q&A article, we have discussed the Jolly Jack's navigation conundrum and answered common questions about the problem. We have also explored the significance of the Jolly Jack's course and how to apply the concepts learned from the problem to real-world navigation.