A pair of perpendicular vectors

[ArcherofScience]

A pair of perpendicular vectors...

√

Homework Statement

This thread contains 2 questions that are similar.

A pair of 482.5 N vectors are perpendicular.
What is the magnitude of their resultant?
Answer in units of N

Two vectors of magnitudes 24 N and 31.1 N
act at right angles to each other.
What is the magnitude of their resultant?
Answer in units of N

Homework Equations

for the first one, what do u exactly do? just find the resultant and that's it? is their a magnitude sign such as north of east or something? do i have to find theta?

for the second one, what does it mean it acts of right angles ot each other? is it just the resultant or what?

The Attempt at a Solution

1st: 482.5 ^2 + 48.5^2= r^2
232806.25 + 232806.25 = r^2
√465612.50=r^2
r= 682.358 <----does it need a positive or negative sign?2nd: 24^2 + 31.1^2 = r^2
576 + 967.21 = r^2
√1543.21= r^2
r= 39.3219 <--- did I even solve this right?

 

[Dick]

√

Homework Statement

This thread contains 2 questions that are similar.

A pair of 482.5 N vectors are perpendicular.
What is the magnitude of their resultant?
Answer in units of N

Two vectors of magnitudes 24 N and 31.1 N
act at right angles to each other.
What is the magnitude of their resultant?
Answer in units of N

Homework Equations

for the first one, what do u exactly do? just find the resultant and that's it? is their a magnitude sign such as north of east or something? do i have to find theta?

for the second one, what does it mean it acts of right angles ot each other? is it just the resultant or what?

The Attempt at a Solution

1st: 482.5 ^2 + 48.5^2= r^2
232806.25 + 232806.25 = r^2
√465612.50=r^2
r= 682.358 <----does it need a positive or negative sign?


2nd: 24^2 + 31.1^2 = r^2
576 + 967.21 = r^2
√1543.21= r^2
r= 39.3219 <--- did I even solve this right?

"acting at right angles" or "perpendicular" mean the same thing. And it means you can apply the pythagorean theorem, just like you did. And again, the word "magnitude" means you don't have to worry about signs. I get a slightly different number from you on the second one. Did you punch a calculator key wrong? And don't forget to specify units in your answer.

 

[ArcherofScience]

oh yeah i just realized my mistake, its 39.2837 i believe. but thanks for your help ! i understand it i believe a bit more, just the way it was worded had me a bit pressured.

 

[Dick]

oh yeah i just realized my mistake, its 39.2837 i believe. but thanks for your help! i understand it i believe a bit more, just the way it was worded had me a bit pressured.

You are maybe worrying a bit more than you need to. And yes, I get 39.2837N. Don't forget the units!

 

[Nickie]

I would like to clarify a few things about perpendicular vectors and their resultant.

First, let's define what perpendicular vectors are. Perpendicular vectors are two vectors that intersect at a right angle, or 90 degrees. This means that the direction of one vector is perpendicular to the direction of the other vector.

Now, let's discuss the resultant of perpendicular vectors. The resultant of two perpendicular vectors is a vector that is formed by adding the two vectors together. This resultant vector is also perpendicular to both of the original vectors.

In order to find the magnitude of the resultant, you can use the Pythagorean theorem, as you have done in your attempts. However, the magnitude of the resultant does not need a positive or negative sign, as it only represents the size of the vector, not its direction. The direction of the resultant can be found by using trigonometric functions and the angle between the two original vectors.

In the first question, you have correctly found the magnitude of the resultant vector. In the second question, you need to use the Pythagorean theorem again to find the magnitude of the resultant vector. Remember, the resultant vector is formed by adding the two original vectors together, so you need to use the magnitudes of both vectors in your calculation.

I hope this helps clarify the concept of perpendicular vectors and their resultant. Remember, as a scientist, it is important to fully understand the concepts and principles behind the calculations, rather than just blindly solving equations.