Can the Dot Product Determine Maximum Distance from the Origin?

  • Thread starter Thread starter jimmy42
  • Start date Start date
  • Tags Tags
    Max Vectors
AI Thread Summary
The discussion revolves around using the dot product of a vector A with itself to determine the maximum distance from the origin. It is established that the square of the distance can be represented as distance² = A·A, and for maximum distance, the derivative A'·A must equal zero, indicating that the velocity vector A' is perpendicular to the position vector A. This condition signifies a turning point in the distance function, confirming that the distance is at a maximum. Participants express confusion about the relationship between perpendicular vectors and maximum distance, but it is clarified that the zero derivative condition indicates a turning point. Overall, the method discussed is validated as a correct approach to finding maximum distance.
jimmy42
Messages
50
Reaction score
0
Hello,

If I have a vector A and then I do the dot product on itself so A°A. Then can I use that to find the maximum distance from the origin? If I take the derivative of the dot product then can I know at what time the maximum distance was travelled?

I have done this but it is wrong based on the graph I made using Wolfram Alpha, I just need some reassurance that I'm on the right track.
 
Physics news on Phys.org
hello jimmy42! :smile:

your method looks ok …

distance2 = A.A,

so if the distance is a maximum, then A'.A = 0

ie A' is perpendicular to A
 
Why if A'.A =0 is the distance a maximum?

I too have a question on this, and I'm failing to see why if the position vector and the velocity vector are perpendicular then the distance is a maximum if the above holds true.

Cheers in advance

Smithy
 
Welcome to PF!

Hi Smithy! Welcome to PF! :smile:
smith873 said:
Why if A'.A =0 is the distance a maximum?

Because that's the derivative of the distance squared (divided by 2),

so it must be 0 if the distance squared is at a turning-point (maximum minimum or inflection point). :wink:
 

Thread 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
View full post »
Thread 'A cylinder connected to a hanging mass'

Thread 'A cylinder connected to a hanging mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
View full post »

Similar threads

Can terminal velocity be determined from the information given?
Replies
7
Views
127
How Do Four-Vectors with Orthogonal Dot Products Determine Each Other's Nature?
Replies
16
Views
1K
B Confused about dot product multiplication
Replies
33
Views
4K
Estimating damped harmonic oscillator parameters from this plot of the oscillations
Replies
9
Views
2K
Projectile Motion Using Vectors
Replies
39
Views
4K
Minimum distance between balls connected by rods
Replies
9
Views
2K
Magnetic field at origin due to infinite wires and semicircular turn
Replies
3
Views
2K
Can I use a dot product of accel. and vel. to find displace.
Replies
1
Views
1K
Given value of vectors a,b, b.c and a+(b×c), Find (c.a)
Replies
5
Views
2K
Max Speed to Move from Point A to Point B
2
Replies
53
Views
5K

Hot Threads

Recent Insights

Back
Top