1. Created by: Jeffrey Bivin Edited by: Aaron Rogers jeff.bivin@lz95.org
Vector Applications
Created by: Jeffrey Bivin
Edited by: Aaron Rogers
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
plane
wind
result

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

5. Joey is playing tug of war with his two best friends
Joey is playing tug of war with his two best friends. He is pulling with a force of 60N at 210o. Simon 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. A 10,000 pound object is suspended on a wire tied to two poles
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
10000 lbs
22o
49o f1 f2

9. 10000 lbs
22o
49o f1 f2

10. Put in a Matrix and use A-1B or can use RREF
10000 lbs
22o
49o f1 f2
Put in a Matrix and use A-1B
or can use RREF

12. A 500 lb cart sits on a ramp inclined at 23o
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

13. A 1500 lb cart sits on a ramp inclined at 18o
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

14. 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
𝑤𝑜𝑟𝑘   =   𝒇𝒐𝒓𝒄𝒆  · 𝒅𝒊𝒔𝒕𝒂𝒏𝒄𝒆
20 ft.

15. 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
𝑤𝑜𝑟𝑘   =   𝑓𝑜𝑟𝑐𝑒  · 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒
20 ft.

16. 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
𝑤𝑜𝑟𝑘   =   𝑓𝑜𝑟𝑐𝑒  · 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒
15 ft.

17. 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 13o above the horizontal. Find the work done on the crate.
40 ft.
35 lbs
𝑤𝑜𝑟𝑘   =   𝑓𝑜𝑟𝑐𝑒  · 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒
13o

18. 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 13o above the horizontal. Find the work done on the crate.
35 lbs
𝑤𝑜𝑟𝑘   =   𝑓𝑜𝑟𝑐𝑒  · 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒
13o
Note: The force is in the same direction of the movement. Therefore, all the force is moving the crate.

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

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

22. 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
𝑤𝑜𝑟𝑘   =   𝑓𝑜𝑟𝑐𝑒  · 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 f

23. 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
𝑤𝑜𝑟𝑘   =   𝑓𝑜𝑟𝑐𝑒  · 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 f

24. 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 13o above the horizontal. Find the work done on the crate.
35 lbs
13o
𝑤𝑜𝑟𝑘   =   𝑓𝑜𝑟𝑐𝑒  · 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 f
13o

25. 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 13o above the horizontal. Find the work done on the crate.
35 lbs
𝑤𝑜𝑟𝑘   =   𝑓𝑜𝑟𝑐𝑒  · 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒
13o
Note: The force is in the same direction of the movement. Therefore, all the force is moving the crate.