The math story problem that would ensue if a carnival ride catastrophically failed


It could use a better explanation (show your workings!). I get slightly different values (maybe rounding errors though).

The time taken to fall is found by solving: s = ut + at^2

s(height) = 35.4; u(initial vertical velocity) = 40.3 sin45; a(gravity) = -9.8 m/s^2
Solve this to get t = 6.9 seconds of flight time

Horizontal velocity is a constant 40.3 cos45 = 28.5 m/s, if we ignore air resistance (it’s equal to the initial vertical velocity in this case).
Distance travelled is 6.9*28.5 = 197 m

This is important since it means you may be lucky enough to miss the road and land on the path, saving you from being arrested for speeding in an unlicensed vehicle, since your terminal velocity (this is a pun) is 39 m/s vertically and 28.5 m/s horizontally, or 48 m/s in your direction of travel.

This is the first time I’ve solved a quadratic equation in many years. Good to see my education wasn’t entirely worthless.

Edit: I think I’ve been sniped:

The problem here is that he uses the maximum speed and assumes that it’s the same at all positions in the arc. It’s only at that maximum speed at the very bottom of the swing.

And by his illustration, he uses a 45 degree angle at the top half of the trajectory when you’ll probably get more distance from the bottom half of the swing due to the greater velocity… Maybe. I’d have to think about it a little more. But later, I don’t want to get sniped either.

(edit fixed spelling)

The Booster Maxx is balanced with a gondola at each end, so I don’t think differences in speed would be an issue.

Edit: the gondolas themselves turn around, so unless they’re balanced you might be able to get a trebuchet effect to increase the distance a little.

Thanks, I am so glad that I resisted the snipe temptation to figure the velocity loss for a given height. I’d assumed that it wasn’t counterbalanced otherwise why would it swing back and forth?

Well, no, I actually did put pencil to paper but didn’t write it up here.

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