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Build your own Simulator: Boats Colliding - Understanding Time as a Parameter
Scenario: Two ships are sailing in the fog and are being monitored by tracing equipment. As they come into the observer's rectangular radar screen, one ship, the Rusty Tube, is at a point 900 mm to the right of the bottom left corner of the radar screen along the lower edge. The other ship, the Bucket of Bolts, is located at a point 100 mm above the lower left corner of that screen. One minute later, both ships' positions have changed. The Rusty Tube has moved to a position on the screen 3 mm left and 2 mm above its previous position on the radar screen. Meanwhile, the Bucket of Bolts has moved to a position 4 mm right and 1 mm above its previous location on that screen.
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. |
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Why I like this Problem and some Good Questions One pair of starting coordinates to get the boats to collide:
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Algebraic Solution
Rusty Tube's starting co-ordinates are (900,0). === Bucket of Bolts starting co-ordinates are (0,100). Put the equations together and find their intersection on the x-axis. 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 === BB starts at 0 and travels horizontally x=+4 each minute, so 545.45=0+4t === Since 118.18 ≠ 136.36 , the boats will not collide. Answer adapted from Dan M |
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Related Topics: Linear Systems; DIY Simulator of Free Fall plus Constant Horizontal Speed |
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Home > Do Mathematics -> Algebra 1 -> Systems of Linear Functions -> DIY Simulator of Boats Colliding |
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