Math Is Fun Forum

I have this theory about collisions, but it's not gaining momentum.

How reliable do you think the search result that this provides is?

So far I've been impressed. When I used to look through the first handful of search results there was sometimes one or more that wasn't quite right. Now, my first result is the AI one and so far it's always seemed correct.

Is the AI result taken from the other ones, a distillation of these? If so, how does the AI know which of the other ones are valid, which are not?

I do a push-up. I push down on the ground; the ground pushes up on me.

I’m trying to relate this to water bottle rockets, where you part fill a plastic bottle with water, cork it, then pump air through a hole in the cork until the air pressure inside is great enough to push the water out and the bottle takes off like a rocket.

Relating this to me doing a push-up; am I the air and the water is the ground?

The air pushes down on the water like me pushing down on the ground (until the water forces the cork out and the water empties from the bottle) and the water pushes back up on the air like the ground pushing back up on me (causing it -and the bottle that contains it - to take off in the opposite direction)?

BBC Bitesize introduced me to Newton’s 2nd Law of motion by way of F=ma. After a few examples of that they introduced the topic of intertial mass by way of a rearrangement of the above formula (F=ma becoming m=F/a). They said the mass in m=F/a is inertial mass, i.e, a measure of how difficult it is to change the velocity of an object.

This seemed to me to imply, that the m in m=F/a was somehow different from the m in F=ma. But if the formula has simply been rearranged it would seem that the m is the same in both versions?

Is the m in F=ma also inertial mass?

I’m trying to apply Gauss’s formula for adding consecutive integers to the first second of a freefalling object.
The formula is n(n+1)/2
E.g, to add the numbers 1 to 100 we do,
n=100
100(100+1)/2
=100(101)/2
=10100/2
=5050

*

During the first second of freefall an object, I’m told, averages a velocity of 5m/s downwards (is this the average of Om/s and 5m/s?) *edit*; (is this the average of 0m/s and 10m/s, not the average of 0m/s and 5m/s)
I’m assuming that one way to get this average would be to divide that first second into tenths, add the ten corresponding velocities, and divide by 10.
So for the first tenth we would reach 1/10m/s, for the second tenth we would reach 2/10m/s, etc, up to the tenth tenth where we reach 10/10m/s.
Using Gauss’s formula for the addition we get;
n(n+1)/2
n=10
=10(10+1)/2
=10(11)/2
=110/2
=55
Which we divide by 10 as we’re talking about tenths, so we get 5.5
But the average velocity for the first second of freefall is 5m/s, not 5.5m/s.
Where am I going wrong

I got a grade 7. Google tells me that's equivalent to an A in old money. I'm happy with that.

Thanks to Bob, KerimF, and everybody else for the help and encouragment. Cheers!