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← 04ps-11 Safety on a Ship

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Showing Revision 1 created 07/03/2012 by Amara Bot.

  1. This problem involves staying safe on a ship. Now let me explain the scenario to you.
  2. The bad guys have taken over the pier, as we can tell by the flag saying "bad guys."
  3. They have a cannon which they can adjust to any angle they want between zero and 180°,
  4. and it can fire cannonballs with the velocity of 56 m/s.
  5. Next to the cannon, there's this flagpole and it has a known height of 30 m.
  6. Now let's say we want to keep an eye on the bad guys and make sure we know what they're up to,
  7. but we don't want to get to within range of their cannon.
  8. We don't want to be able to be shot by this cannon. It is not fun. So what do we need to do?
  9. Well first, we need to calculate the range of the cannon to figure out how far this thing can shoot
  10. and as a hint ranges optimized from this angle is equal to 45°, but what then?
  11. What do we do after we've calculated the range of the cannon?
  12. Well, we need keep our distance, but how do we do that? How do we know our distance?
  13. Well, lucky enough there is this flagpole.
  14. If we look from the top of this flagpole to the bottom, we can measure this angle β,
  15. and as long as β is pretty small, let's say it's less than 10°, these are going to be
  16. very close to right angles and we can do some trigonometry.
  17. Now clearly if the boat is really close to the shore, this flag pole will look very big.
  18. They would be large to our observer, and if the boat is very far away they would be small.
  19. The flagpole will look very small from faraway.
  20. I want to know at what value of β can a cannon reach our ship.
  21. Now this is a really tricky question.
  22. It involves a pretty complicated 2-dimensional motion problem as
  23. well as some trigonometry that we learned in the first unit.
  24. If you can put these all together and get the correct answer, I'll be very impressed.