Flash MX 2004 Games : Art to ActionScript

Flash MX 2004 Games
Instead of using lots of if conditions we can use a simple physics calculation. The Y value for a projectile
motion is defined as:
y = ut + gt 2
where u is the launch value, t is the time in seconds and g is the value of gravity. If time, t, is less than
a second the value for t 2 will be less than t, but above one second, t 2 will overtake. If g operates in
the opposite direction to u then the increase in the values for y will decrease and eventually reverse.
But this may seem all very hit and miss. Actually it is easy to calculate. Suppose that you want a jump
to occur over one second and the starting and ending values for y are zero, then you want:
ut =−gt 2
when t = 0 and t = 1. To do this you need to solve a quadratic equation. Whoops, that sounds like
maths! But believe me, it is not that hard. You want:
ut + gt 2 = 0
But you also want to control the maximum height of the jump. This occurs when the derivative
of the curve has a value of zero. The derivative of the curve is:
u + 2gt
OK, so let’s fiddle with the figures. If we want a maximum height for the curve of 150 and if the
total jump takes one second then the maximum height is going to be at 0.5 seconds; in other words,
half way through the jump. At t = 0.5 we want:
u + 2gt = 0 and ut + gt 2 = 150
Replacing t with 0.5 gives:
u + g = 0 and 0.5u + 0.25g = 150
Two equations with two unknowns can be solved: u =−g from the first equation therefore we can
substitute u for −g in the second equation giving −0.5g + 0.25g = 150 or 0.25g = 150; which means
that g =−600 and u = 600.
If you are working in metres rather than pixels then the usual value for g is −9.81 ms 2 but for
convenience we will call this −10 ms 2 . Imagine that the cat is about one metre tall and can jump just
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