PROJMOT.81 (Projectile Motion) Freeware
by Daniel Bishop (danb2k@hotmail.com) 2000-10-09

Given the acceleration due to gravity, the initial velocity, the angle, and the initial height, this program solves for the time it takes for a projectile to hit the ground, its maximum height, and its horizontal range.

Prgm_:PROJMOT
:Disp "GRAV. ACC."
:Input G
:Disp "INIT VELOCITY"
:Input V
:Disp "ANGLE"
:Input \theta\
:Disp "INIT. HEIGHT"
:Input Y
:(V(sin \theta\)+\sqrt\((Vsin \theta\)²+2G))/G\->\T
:(Vsin \theta\)²/(2G)+Y\->\H
:VTcos \theta\\->\X
:ClrHome
:Disp "T="
:Disp T
:Disp "MAX HEIGHT="
:Disp H
:Disp "HORIZ. RANGE="
:Disp X

Symbols used:
\theta\ = the Greek letter theta, [ALPHA][3]
\sqrt\ = square root symbol, [2nd][x²]
\->\ = STO key

Sample run:
GRAV. ACC.
?9.8               // acceleration due to gravity is 9.8 m/s
INIT. VELOCITY
?10                // user input: initial velocity is 10 m/s
ANGLE
?45°               // user input: projectile is fired at an angle of 45° above horizon
INIT. HEIGHT
?5                 // user input: initial height of projectile is 45° above

T=
      1.96291764   // projectile hits ground 1.96 s after being fired
MAX. HEIGHT=
     7.551020408   // maximum height is 7.55 m
HORIZ. RANGE=
     13.87992374   // horizontal range is 13.9 m

Notes:
* Output is affected by whether calc is in Rad or Deg mode.
* Air resistance and all other force except gravity are ignored in this model.
* All values must have coherent units, i.e., if g is is m/s², then V must be in m/s and the height and horizontal range will be in meters.