The speed of a motorcycle "around" a truck

[Yanick Toutain]

"For 10 hours the passenger of a truck sees a motorcycle circling around the truck.
The passenger calculates that the revolution speed of the motorcycle is
v = 1 km/h
But there you go... the truck is not stationary. During these ten hours, the truck drove at a speed
S = 100 km/h
The question is (obviously in relation to the road)
what is the length of the motorcycle's journey.
And so what was the average speed of the motorcycle?
And so what is the simple formula giving the value of T - S (according to S and v)

(do not ask what the radius of revolution or the period is, this data is useless to answer the question)

Subsidiary question: Does the approximate formula giving the result and/or the rigorous demonstration appear somewhere in a physics work for 3 centuries?"

[Yanick Toutain]

Those who are destabilized by the absence of a radius in the problem statement can choose the value of their choice.
Any value will give the answer.
You can choose R = 5 / %pi (km) if you want.
By placing the motorcycle at a distance x = 1.59155 km (in front of the truck located at x = 0) at the start of the problem.

[Sylvia Else]

Sounds simple enough in concept. Let the truck be moving in the y
direction. Express the x and y components of the motorcycle's velocity
relative to the truck as function of time. Add the trucks velocity to
the y component. Use Pythagoras to get the motorcycle's speed relative
to the ground as a function of time. Now integrate with respect to time.

Without having written anything out, it seems to me that this is a
ghastly thing to integrate. Maybe there's an analytical solution. Maybe
not. But either way, it's just math, and not particularly interesting in
a physics group.

Perhaps that's why you've got no takers.

Sylvia.

[Yanick Toutain]

Thank you for your participation
Everything you wrote is correct
But I've known the answer for years, having found the formula giving the result when v is much smaller than S
Some participants in fr.sci.math and sci.math try to find the answer
What I want is a rigorous demonstration from the point of view of a cantorist mathematician

Because what happens next is going to be exciting.
When I ask what are the successive accelerations of the motorcycle.
And the physical consequences of what will then be stated.
I dialogue constructively with Bard (who presented a demonstration) and ChatGPT (who corrected Bard's result at my request)

The first question is therefore: what simple formula gives T - S
The additional speed of the motorcycle compared to the truck


Subsequently, I think I will trigger a storm of anger among physicists!
(Google Translate)

[Sylvia Else]

OK, now you're starting to look delusional. It's just coordinate
geometry and calculus. If you can do the math, then do it. If not,
perhaps someone else will do it for you. But it's not particularly
interesting, and your belief that you'll upset physicists with the
result is not credible.

Sylvia.

[Yanick Toutain]

end "your belief that you'll upset physicists with the
result is not credible."

start "OK, now you're starting to look delusional. It's just coordinate
geometry and calculus"

In summary, you insult me, but you insult me without being upset
And before I even warned you that I was the executor of Isaac Newton's will

If you don't try to give the answer, go insult someone else somewhere else.

[Physfitfreak]

You missed the last paragraph in that reply to Yank Tutankhamun:

"In other words, fuck you!"

That would complete your reply to him.

[Yanick Toutain]

For 10 hours the passenger of a truck sees a motorcycle circulating around the truck.

The passenger calculates that the revolution speed of the motorcycle is
v = 1 km/h
But there you go... the truck is not stationary. During these ten hours, the truck drove at a speed
S = 100 km/h
The question is (obviously in relation to the road)
what is the length of the motorcycle's journey.

And so what was the average speed of the motorcycle T?

And so what is the simple formula giving the value of T - S (according to S and v)

(do not ask what the radius of revolution or the period is, this data is useless to answer the question

So you can choose R=5/pi km or any other value )