1 Dimensional Trajectories
 
In these examples we are studying the motion of particles in a constant gravitational field.  The graphs show the height of a trajectory over the distance it traveled.  The data used for these diagrams was produced by program j5 which is written in Fortran 90. These diagrams were produced by the program Plot.   
 
Equations Visualized: 
  • y(t) = y(0) + vy(0)*t + .5*g*t2 
  • x(t) = x(0) + vx(0)*t 
"y" is vertical distance, "x" is horizontal distance, "t" is time, "g" is acceleration due to gravity, "vy(0)" = v*sin(angle) is initial vertical velocity, where "v" is initial speed, and "vx(0)"= v*cos(angle) is initial horizontal velocity
 

 
This diagram stops the time at a specific point showing how far and how high the trajectories have gone over that period of time.  Each color represents a trajectory shot into the air at a different angle.  "Y distance" is height and "x distance" is horizontal distance traveled.
 
 
 
This diagram allows time to continue until all the trajectories hit the ground (height 0), showing their complete paths.  We added graphics (cannonball-an example of a trajectory, and the UCLA logo) to this diagram using MacDraw. 
 
program j5  
      integer :: i  
      integer, parameter ::length=24  
      real :: g=-9.8, vyi=0, vxi=0, yi=0, xi=0, vi, theta  
      character*40 :: prompt = 'enter vi and theta'  
      real, dimension(length) :: y, t, x  
      print *, prompt  
      read (*,*) vi,theta  
      write (7,*) '# shooting cannon w/ velocity',vi,' angle',theta  
      theta=theta*6.2831853/360.  
      vxi=vi*cos(theta)  
      vyi=vi*sin(theta)  
      write (7,*) 'y_distance', ' x_distance ', 'time'  
      do i=1,length  
         t(i)=i-1  
         y(i)=yi+vyi*t(i)+.5*g*t(i)**2  
         x(i)=xi+vxi*t(i)  
         write (7,*) y(i), x(i), t(i)  
      end do  
      print *, 'vxi=', vxi, 'vyi=', vyi  
      print *, y  
      end program j5  

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