Problem setting: 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. Using graphs and equations, find out if the two ship will collide.
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| Algebraic solution to original question
Rusty Tube's starting co-ordinates are (900,0).
Bucket of Bolts starting co-ordinates are (0,100).
Put the equations together and work out where on the x-axis their journeys will cross.
We do not need the value of y at this point for the problem, but it is:
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 \ne 136.36 , the boats will not collide.
Answer adapted from Dan M
|One answer to getting the boats to collide:
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