Estimation of Landing Time
>
> PLOT4 := display(
> {
> plot_motion( SOLN, [0..180], scale[XV], xtickmarks=3 ),
> textplot( [ [ 40, 1.1, `x/1000` ],
> [ 40, -0.9, `v/10` ] ] )
> },
> title="Position and Velocity: The First 3 Minutes" ):
> display( PLOT4 );
>
> PLOT5 := display(
> {
> plot_motion( SOLN, [150..170], scale[X], xtickmarks=3 ),
> textplot( [ [ 152, 60, `x` ] ] )
> },
> title="Estimation of Landing Time" ):
> display( PLOT5 );
>
From the last plot, it appears that landing occurs near t=162 seconds.
> SOLN( 0 ): # reset numerical integrator to initial time
> SOLN( 162 );
![[Maple Math]](images/parachute-ijee56.gif){kind=small}
>
Since, by this time, the motion is essentially linear, an improved estimate of the landing time can be obtained by linear interpolation:
> t_new := 162 - subs( SOLN(162), x(t)(162)/v(t)(162) );
![[Maple Math]](images/parachute-ijee57.gif){kind=small}
>
As a final cross-check:
> SOLN( 161.764 );
![[Maple Math]](images/parachute-ijee58.gif){kind=small}
OK, so it's not exactly zero but this height is only 2 cm, less than one inch!
>