Treasure Hunt: Adding Vectors for Displacement

In summary, a vector is a mathematical quantity with both magnitude and direction. To add vectors for displacement, determine the direction and magnitude of each vector, use the Pythagorean theorem to find the resultant vector, and use trigonometric functions to find the angle. Displacement and distance differ in that displacement is a vector representing change in position while distance is a scalar representing total length of path. Vectors can be added in any order, but the direction and magnitude of the resultant vector will vary. In treasure hunting, adding vectors for displacement is important for accurately determining the direction and distance of the treasure, potentially saving time and avoiding obstacles.
  • #1
shimmer71
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You are on a treasure hunt and your map says "Walk due east for 52 paces, then walk 29.6° north of west for 44 paces, and finally walk due north for 25 paces."
(a) What is the magnitude of the component of your displacement in the direction due north?
b) What is the magnitude of the component of your displacement in the direction due east?
 
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  • #2
what have you done on this problem
 
  • #3
You are expected to try! Show us what you have tried already and we will know better what hints will help you.
 

1. What is a vector?

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

2. How do you add vectors for displacement?

To add vectors for displacement, you must first determine the direction and magnitude of each vector. Then, you can use the Pythagorean theorem to calculate the resultant vector. Finally, use trigonometric functions to find the angle of the resultant vector.

3. What is the difference between displacement and distance?

Displacement is a vector quantity that represents the change in position of an object, while distance is a scalar quantity that represents the total length of the path traveled by an object. Displacement takes into account the direction of movement, while distance does not.

4. Can vectors be added in any order?

Yes, vectors can be added in any order. This is because the resultant vector is independent of the order in which the vectors are added. However, the direction and magnitude of the resultant vector will vary depending on the order in which the vectors are added.

5. What is the importance of adding vectors for displacement in treasure hunting?

Adding vectors for displacement is important in treasure hunting because it allows you to accurately determine the direction and distance of the treasure from your current location. This can save time and effort in finding the treasure, as well as help you avoid obstacles or hazards along the way.

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