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_scienceMathsChuteLibre

Retrieve some parameters from equations hourly of an object in free fall under only the force of a gravity field.

Equation hourly of the speed from to time :
V(t) = -gt + V0

Equation hourly of the altitude relative to time :
Z(t) = -1/2gt² + V0t + Z0

With g is the standard gravity, V0 is the initial speed and Z0 is the initial height.

The trajectory is a right line possibly in two-way (downwards only or upwards then downwards), in the same plane. The rules are as follows :

• a vertical movement, the unit vector pointing upwards;
• the time is in seconds;
• the height (altitude) is in meters;
• the speed is in meters by second (m.s-1).

The result depends on the value of the flag.

Prototype :

fun [F F F I F] F

• F : g : the standard gravity. Can be nil, in this case, the default value will be 9.8 m.s-2 (its an average value on Earth).


• F : V0 : the initial speed. If positive, the object goes to up in the first time, if negative, the object goes to bottom. Can be nil, then this value will be 0.0.


• F : H0 : the initial height (altitude). Can be nil, then this value will be 0.0.


• I : a flag :
  • SCOLMATHS_MVT_GETSPEED_TOTIME : get the speed from to the time
  • SCOLMATHS_MVT_GETTIME_TOSPEED : get the elapsed time from to the speed
  • SCOLMATHS_MVT_GETHEIGHT_TOTIME : get the height from to the time
  • SCOLMATHS_MVT_GETHEIGHT_TOSPEED : get the height from to the speed
  • SCOLMATHS_MVT_GETSPEED_TOHEIGHT : get the speed from to the height
  • SCOLMATHS_MVT_GETTIME_TOHEIGHT : get the elapsed time from to the height


• F : a parameter. It depends on the flag. Can be nil, then this value will be 0.0.
  By example, if the flag is SCOLMATHS_MVT_GETSPEED_TOTIME then this parameter is the time (2.0 for t=2 seconds).

Return : F the result or nil if error

See also :

Example :

Get the height after 1 second. The initial speed is 2 m/s and the initial height is 5.5 meters. The result is 2.6 meters.

fun main ()=
	_showconsole;
	_fooF _scienceMathsChuteLibre nil 2.0 5.5 SCOLMATHS_MVT_GETHEIGHT_TOTIME 1.0; // 2.600000
	0;;

Note

Results are approximations (depends on float definition)