A group of soldiers walked 15km north from their camp then covered 10km more due east.

1. What is the total distance walked by the soldiers?
2. Define the displacement?

Find the resultant displacement of the car: 30 km, South and 50 km

West.

1. To find the total distance walked by the soldiers, you need to calculate the magnitude of their displacement. This can be done using the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle (c) is equal to the sum of the squares of the other two sides (a and b). In this case, we can consider the north direction as side a, the east direction as side b, and the displacement as the hypotenuse side c.

a^2 + b^2 = c^2

In this scenario, the north direction is 15 km and the east direction is 10 km. Substituting these values into the formula:

(15 km)^2 + (10 km)^2 = c^2

225 km^2 + 100 km^2 = c^2

325 km^2 = c^2

By taking the square root of both sides:

c ≈ √325 km

c ≈ 18.03 km

Therefore, the total distance walked by the soldiers is approximately 18.03 km.

2. Displacement, in physics, refers to the change in position of an object from its initial point to its final point in a straight line. It is a vector quantity, meaning it has both magnitude and direction. In this scenario, the displacement of the soldiers can be represented by a single straight line connecting their initial position at the camp to their final position after walking north and then east. The magnitude of the displacement, as calculated above, is approximately 18.03 km, and the direction can be described as northeast.

To find the total distance walked by the soldiers, you can use the concept of vector addition or the Pythagorean theorem if the walking path forms a right-angled triangle.

1. Using vector addition:
- Draw a diagram to represent the soldiers' journey.
- Draw a line segment of 15 km in the north direction from the camp. This represents their initial displacement.
- Then, draw another line segment of 10 km in the east direction from the endpoint of the first line. This represents their second displacement.
- Now, you can visually see that the soldiers have formed a right-angled triangle with the camp at one corner.
- To find the total distance walked, draw a straight line from the camp to the endpoint of the second displacement. This line represents the total distance walked by the soldiers.
- Measure this line using a ruler or a scale, and you will find the total distance walked.

2. Using the Pythagorean theorem:
- As explained above, the soldiers' path forms a right-angled triangle.
- The first displacement of 15 km to the north can be considered the length of one side of the triangle (let's call it side A).
- The second displacement of 10 km to the east can be considered the length of the other side of the triangle (let's call it side B).
- Therefore, the total distance walked, which is the hypotenuse of the triangle, can be found using the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.
- Calculate the square of side A (15^2), the square of side B (10^2), add them together, and then find the square root of this sum. The result will be the total distance walked by the soldiers.

Now, let's answer your questions:

1. To find the total distance walked by the soldiers, you can visually analyze the displacement vectors formed by their journey or calculate it using the Pythagorean theorem. Based on your diagram or calculation, you'll find the total distance walked by the soldiers.

2. Displacement refers to the change in the position of an object, measured in a straight line from the initial position to the final position. In this case, the soldiers' displacement would be a straight line drawn between their initial camp position and the final endpoint of their journey.

1. the distance is ... 15 km + 10 km

2. the displacement is a vector from their starting point to their finishing point

use Pythagoras and trig to find the distance and direction