Newsy Letters and Publications
Home > Do Mathematics -> Algebra 1 -> DIY Simulator of Boats Colliding
Build your own Simulator: Boats Colliding - Understanding Time as a Parameter
Question: Assume that both ships continue to move at a constant speed on their respective linear courses. Graph this problem. Can you see on the graph what is happening? Now, create a simulator that animates the boats using time and find out if the two ship will collide. Then show algebraically what is happening with equations.
1. Open GeoGebra (http://geogebra.org)
2. Change the graphics view to fit the 2 starting points.
2a. Put (0,0) down by the bottom left corner and zoom-out so that the window is (1100,800).
2b. Turn the grid on. (Help is coming for this.)
3. Input point A. Click in input window and type: A=(900,0) and hit Enter.
4. Input point B. Type: B=(0,100) and hit Enter.
5. Input point At1. Type: At1=A+(-3,2) and hit Enter.
6. Input point Bt1. Type Bt1=B+(4,1) and hit Enter.
7. Input line a. Type line[A,At1] and hit Enter.
8. Input line b. Type line[B,Bt1] and hit Enter.
The animated simulator
9. Input number t. Type t=0 and hit Enter.
10. Make t a slider. Right-click on t in algebra window. Select "Properties". Click & drag the properties box down a bit.
10.a On the Basic tab, select "Show object". (Slider should appear in graphics window.) Check that "Show label" is selected.
10.b On the Slider tab: min=0, max=200, increment=1, width=400, repeat=increasing.
10.c Click on Close.
11. Input point At. Click in input window and type: At=A+t*(-3,2) and hit Enter.
12. Input point Bt. Type Bt=B+t*(4,1) and hit Enter.
Right-click on the slider t and select: Animation on.
Rusty Tube's starting co-ordinates are (900,0).
Moves by (-3,+2) so the slope (gradient) is 2:-3=-0.6667
This means the equation is y=-0.6667x+c .
Substituting y=0 and x=900 , 0=600+c or c=600 .
So the equation of RT's journey is y=-0.6667x+600 .
Bucket of Bolts starting co-ordinates are (0,100).
Moves by (+4,+1) so the slope (gradient) is 1:4=0.25 .
Which means the equation is y=0.25x+c .
Substituting y=100 and x=0 , 100=0+c or c=100 .
So the equation of BB's journey is y=0.25x+100 .
Put the equations together and find their intersection on the x-axis.
That is, solve 2x2 system of linear equations: y=0.6667x+600 and y=0.25x+100 .
Set them equal and solve for x:
We do not need the value of y at this point for the problem, but it is: y=0.6667x+600 where x=545.45 So: y=236.37
Now find the time taken for each boat to get there and if they are the same they will collide.
RT starts at 900 and travels horizontally x=3 each minute, so 545.45=900-3t
Solving for t: t=354.545/3 or t=118.18 [min]
BB starts at 0 and travels horizontally x=+4 each minute, so 545.45=0+4t
Solving for t: t=545.45/4 or t=136.36 [min]
Since 118.18 ≠ 136.36 , the boats will not collide.
Related Topics: Linear Systems; DIY Simulator of Free Fall plus Constant Horizontal Speed
lgebra, distance, speed, time, DST, linear functions, simulator geogebra, application, geometry, program
help on how to format text