# Back to Rotorua

Last Friday I skived off work (well, I took a day’s leave) – it was the last day of the break between our semesters and the last chance for a day off work for a while – and went luging again. But this comment doesn’t concern the luge, rather the sky swing which is located at the top of the gondola in Rotorua. For those of you haven’t seen it – it’s like a conventional playground swing, though rather bigger – you get strapped in, and then mechanically hauled up a rather frightening distance, and you let go. Once you’ve swung for a bit, they slow you down and let you off.

Now – has anyone else noticed the entirely proposterous sign at the bottom of the swing? It says 0 to 150 kmh in 2 seconds.  One hundred and fifty kilometres an hour? I beg to differ, and here’s why.

The swing is powered entirely by gravity. And the best way of getting gravity to move you is through freefall – where the movement is in the same direction as the force (that’s the ‘dot’ bit in the integral of F dot dx, for those of you who know what I’m talking about).  Gravity gives you a freefall acceleration of about ten metres per second every second. So, if released at rest, you will be moving at 10 metres a second after one second, and 20 metres a second after two seconds, and so on.

Twenty metres a second times 3600 seconds per hour gives us 72 thousand metres an hour, or 72 kilometres an hour, after 2 seconds freefall.  This is way off the 150 kmh that the swing advertises. Plus, the swing is less effective than freefall, because for most of the swing the force (gravity) is closer to perpendicular to your direction of travel, rather than parallel with it. So we will be talking less velocity than this when the swing is at the bottom, which is where it moves the fastest (and where, incidently the passengers will feel the largest force.)

So, it might be more like 70 kmh, but even so you wouldn’t get me going on it.