# Gravity Simulation in SCI

Gravity Simulation in SCI

Standard gravitational acceleration is 9.8 m/s/s. To convert this to the SCI simulation units of pixels/cycle/cycle, we use the following formula

SCI Code:
`	g = 9.8 * h/(f ** 2)`

where

h is the height, in pixels, of a one meter tall object

f is the frequency, in cycles/second, of the animation cycles

Normal animation speed is 10 animation cycles/second, so in general this reduces to

SCI Code:
`	g = .098 * h`

A standard sized actor is about 33 pixels tall. Assuming that the actor is a meter tall, we get a default g of

SCI Code:
```	g = 3.23
= 3```

### JumpTo

The JumpTo motion class is designed to allow an actor to jump to a certain point on the screen. This is done by assuming that, in the Jump class, the horizontal and vertical speeds are related by the scale factor n. We then solve for the magnitude which gets us where we want to go.

The x coordinate of the endpoint is given by

SCI Code:
`	x1 = x0 + v * t`

so that

SCI Code:
`	t = (x1 - x0)/v`

The y coordinate is given by

SCI Code:
```	y1	= y0 + n * v * t + g * t**2/2

= y0 + n * v * (x1 - x0)/v + g * (x1 - x0)**2/(2 * v**2)```

writing

SCI Code:
```	dx = x1 - x0
dy = y1 - y0```

we have

SCI Code:
`	dy - n * dx = g * dx**2/(2 * v**2)`

so that

SCI Code:
`	v = sqrt(g * dx**2/(2 * (dy - dx)))`