Or…how I forgot high school maths
It started with a whimsical comment of mine, during a brief email-chat about the “incredible video [that] shows Hayabusa2 pogo-bouncing off [an] asteroid”
I said my next Blog post would now be where I would ‘Compare the parabolic trajectory of the same rock on Earth vs on this Asteroid.’
It’s this ‘cannon ball’ stuff:
So, 2 or 3 hours of effort later and still I’m going in circles. Just can’t get it to work. It’s actually high-school maths.
The first equation I found (Wikipedia) had an archaic term (sec) which I’d forgotten about:
x is how far along parallel to the ground it has gone, and y is how high it is at that (x) point.
Take 1 : Quick Excel Sanity Check
My first quick attempt in Excel said that after being fired then travelling just 25cm (x), the ball was already 1.3 metres underground (y) Ok, probably not right.
Take 2 : More Careful Excel with Known Result Values
I had a simple example that showed with given input values, the ball would be 0.2 m off the ground after travelling 10 metres; i.e. it’s descended and is nearly on the ground again. I re-did my Excel, more carefully, then entered the same input values as the example:
At 10 metres along (x), my ball is 10.000 (y) metres up…and still rising. Ok, still got a big problem.
Take 3: Go Manual
Pen and Paper. But first…I’d earlier found a site that had the formula written a cleaner way. It’s the ‘same’ as the other one but just had things shuffled about a bit:
So I broke it all down and did each bit by hand, with a calculator. Remembering that after 10 metres, it should calculate being 0.2 metres high…
..and I got 0 metres. I’ve obviously done something wrong.
Sorta Take 4: The Python Program
Excel isn’t actually my favourite tool for doing more complex maths things. I find it easier to write a Python program.
Or, in this case, openly use another person’s code (which they allow). I had to make a few tiny changes. BUT BUT BUT, he’s solving the problem a different way. He’s NOT using the above formula, but basically calculus (!) instead. It’s actually the site I mentioned earlier. This is just some of the code:
But I got it to work and it draws pretty cannon-ball pictures for different angles:
The blue line shows at 10 metres it’s still just off the ground (good!).
I then re-wrote it to show the x,y numbers and it printed out that it was about 0.2 metres high at the 10 m mark (also good)
And that’s where I stand. Tomorrow it’s going to be cold and raining, so no hiking and photography (ironic smile). Instead it’s Take 5.
Update: Mystery solved!