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Vector Applications

Vector Applications. By: Jeffrey Bivin Lake Zurich High School jeff.bivin@lz95.org. Last Updated: February 14, 2011. Find the component form of the vector that represents the velocity of an airplane descending at a speed of 150 mph at an angle of 30 o below the westward horizontal . 210 o.

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Vector Applications

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  1. Vector Applications By: Jeffrey Bivin Lake Zurich High School jeff.bivin@lz95.org Last Updated: February 14, 2011

  2. Find the component form of the vector that represents the velocity of an airplane descending at a speed of 150 mph at an angle of 30o below the westward horizontal. 210o 30o 150 mph

  3. An airplane is traveling at a speed of 600 mph with a bearing of N35oW at a fixed altitude and no wind. As the plane crosses the Mississippi river, it encounters a wind blowing with a velocity of 60 mph in the direction of N40oE. What is the resultant speed and direction of the plane? 60 mph 125o 35o result 40o 50o 600 mph 60 mph 600 mph wind result plane

  4. 125o 35o result 40o 50o 600 mph 60 mph 600 mph wind result plane

  5. Joey is playing tug of war with his two best friends. He is pulling with a force of 60N at 210oSimon exerts a force of 30N at 45o. Austin exerts a force as well. To achieve equilibrium and thus, not lose the game, what is the force Austin must exert and at what angle? 210o 45o 30 N 60 N

  6. 210o 45o 30 N 60 N

  7. 210o 45o 30 N 60 N

  8. 22o 49o 10000 lbs A 10,000 pound object is suspended on a wire tied to two poles. The angle between the horizontal and the wire to the shorter pole is 22o. The angle between the horizontal and the wire to the taller pole is 49o. Find the tension in the cable to each pole. 158o f1 f2

  9. 22o 49o 10000 lbs f1 f2

  10. 22o 49o 10000 lbs f1 f2 Put in a Matrix and use RREF

  11. A 500 lb cart sits on a ramp inclined at 23o. What is the force is required to keep the cart from rolling down the ramp? 500 lbs f 67o 23o 500 lbs Normal Vector Gravity

  12. A 1500 lb cart sits on a ramp inclined at 18o. What is the force is required to keep the cart from rolling down the ramp? 1500 lbs f 72o 18o 1500 lbs

  13. A mover exerts a force of 55 pounds in a horizontal direction on a crate to move it across the floor for a distance of 20 feet. Find the work done on the crate. 55 lbs 20 ft.

  14. A mover exerts a force of 55 pounds at an angle of 45o below the horizontal on a crate to move it across the floor for a distance of 20 feet. Find the work done on the crate. 45o 55 lbs 20 ft.

  15. A sled is to be pulled by a rope at a 37o angle above the horizontal with a force of 63 lbs.. Find the amount of work done to move the sled 15 feet. 63 lbs 37o 15 ft.

  16. A mover exerts a horizontal force of 35 pounds on a crate as it is pushed up the ramp that is 40 feet long and inclined at an angle of 13oabove the horizontal. Find the work done on the crate. 40 ft. 35 lbs 13o

  17. A mover exerts a force of 35 pounds parallel to the ramp on a crate as it is pushed up the ramp that is 40 feet long and inclined at an angle of 13oabove the horizontal. Find the work done on the crate. 35 lbs 13o Note: The force is in the same direction of the movement. Therefore, all the force is moving the crate.

  18. A mover exerts a force of 35 pounds on a crate at an angle of 20o below the horizontals it is pushed up the ramp that is 50 feet long and inclined at an angle of 23oabove the horizontal. Find the work done on the crate. 50 ft. 20o 35 lbs 23o

  19. The following slides are the same examples previously examined that calculate the work needed to move an object. However, an alternative method is demonstrated.

  20. A mover exerts a force of 55 pounds at an angle of 45o below the horizontal on a crate to move it across the floor for a distance of 20 feet. Find the work done on the crate. 45o 55 lbs 45o f

  21. A sled is to be pulled by a rope at a 37o angle above the horizontal with a force of 63 lbs.. Find the amount of work done to move the sled 15 feet. 63 lbs 37o f

  22. A mover exerts a horizontal force of 35 pounds on a crate as it is pushed up the ramp that is 40 feet long and inclined at an angle of 13oabove the horizontal. Find the work done on the crate. 35 lbs 13o f 13o

  23. A mover exerts a force of 35 pounds parallel to the ramp on a crate as it is pushed up the ramp that is 40 feet long and inclined at an angle of 13oabove the horizontal. Find the work done on the crate. 35 lbs 13o Note: The force is in the same direction of the movement. Therefore, all the force is moving the crate.

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