Can the Dot Product Determine Maximum Distance from the Origin?

[jimmy42]

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.

 

[tiny-tim]

hello jimmy42!

your method looks ok …

distance² = A.A,

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

ie A' is perpendicular to A

 

[smith873]

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

 

[tiny-tim]

Welcome to PF!

Hi Smithy! Welcome to PF!

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).