Pythagorean Theorem to find the resultant

In summary, the Pythagorean Theorem is a mathematical principle used to find the length of the hypotenuse in a right triangle. It can also be used to find the resultant of two perpendicular forces by squaring and adding the magnitudes of the forces. However, it cannot be used for non-perpendicular forces and vector addition must be used instead. The resultant found using the Pythagorean Theorem will have the same units as the forces being measured, and it can be used to find the resultant of more than two forces as long as they are all perpendicular to each other.
  • #1
missie
38
0
A man walks 5 blocks east, then turns 10 blocks north, then walks 5 more block east.

Total displacement____?

is it...

10^2 + 10^2 = c^2

(Square root 200)=c^2

14.14 = c^2

is this right?
 
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  • #2
Yes. Try to think of the paths as vectors where you can rearrange them how you choose.

http://www.glenbrook.k12.il.us/GBSSCI/PHYS/Class/vectors/u3l1b.html
 
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  • #3


Yes, your application of the Pythagorean Theorem to find the resultant displacement is correct. The total displacement can be calculated using the formula c = √(a^2 + b^2), where a and b are the lengths of the legs of a right triangle and c is the length of the hypotenuse (resultant displacement in this case). In this scenario, a = 10 blocks and b = 15 blocks, so the total displacement is √(10^2 + 15^2) = √(100 + 225) = √325 = 18.03 blocks. This means that the man's final position is 18.03 blocks from his starting point, in a direction that is 37.38 degrees north of east.
 

Related to Pythagorean Theorem to find the resultant

1. What is the Pythagorean Theorem?

The Pythagorean Theorem is a mathematical principle that states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

2. How is the Pythagorean Theorem used to find the resultant?

To find the resultant of two perpendicular forces, we use the Pythagorean Theorem by squaring the magnitude of each force and adding them together. Then, we take the square root of the sum to find the magnitude of the resultant force.

3. Can the Pythagorean Theorem be used to find the resultant of non-perpendicular forces?

No, the Pythagorean Theorem can only be used to find the resultant of two perpendicular forces. In cases where the forces are not perpendicular, vector addition must be used to find the resultant.

4. What are the units of measurement for the resultant found using the Pythagorean Theorem?

The units of measurement for the resultant depend on the units of measurement for the two forces. If the forces are in Newtons, the resultant will also be in Newtons. If the forces are in pounds, the resultant will be in pounds.

5. Can the Pythagorean Theorem be used to find the resultant of more than two forces?

Yes, the Pythagorean Theorem can be used to find the resultant of any number of forces as long as they are all perpendicular to each other. The process involves finding the resultant of two forces, and then using that resultant as one of the forces in the next calculation.

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