Vector Practice Problems SHOW ALL WORK IN YOUR NOTEBOOK!! 1. A 5.6 m ladder leans against a wall, making an angle of 28.1 degrees with the wall. What is the height above the ground where the ladder makes contact with the wall? 2. The x and y components of a displacement vector are 2.2 m and 7.81 m respectively. What angle does the vector make with the x-axis? 3. If the hypotenuse of a right triangle is 5.47 m and one angle is 20.5 degrees, what is the sum of the other two sides? 4. What is the angle in the figure if h=2.7 cm and b=4.06 cm? 5. A pole is held vertically by attaching wires at a height of 10.8 m above the ground. The other end of each wire is anchored in the ground at a distance of 7.34 m from the base of the pole. The pole makes a right angle with the ground. What is the length of each wire? 6. A hiker walked 3.23 km [E] and 5.13 km [N]. What distance did the hiker walk? 7. A force of 209 N at an angle of 30.3 degrees from the horizontal is used to push on the handle of a lawnmower. What is the horizontal component of the force? 8. A force of 186 N at an angle of 32.6 degrees from the horizontal is used to push on the handle of a lawnmower. What is the horizontal component of the force? 9. A horizontal force of 414 N is required to overcome friction acting on a wagon. If the wagon is pulled by a handle that is at an angle of 60.6 degrees from the vertical, what force must be applied to the handle to overcome friction? 10. If the hypotenuse of a right triangle is 1.98 m and one angle is 37.6 degrees, what is the sum of the other two sides? 11.After walking 11 km due north from camp, a hiker then walks 11 km due east. What is the total distance walked by the hiker? 12. Two boys push on a box. One pushes with a force of 125 N to the east. The other exerts a force of 165 N to the north. What is the size and direction of the resultant force on the box? 13. An explorer walks 13 km due east, then 18 km due north, 3 km east, and finally 5km north. What is the total distance walked? 14. Three teenagers push a heavy crate across the floor. Dion pushes with a force of 185 N at 0 degrees. Shirley exerts a force of 165 N at 30 degrees, while Joan pushes with a 195 N force at 300 degrees. What is the resultant force on the crate? 15. A heavy box is pulled across a wooden floor with a rope. The rope makes an angle of 60 degrees with the floor. A force of 75 N is exerted on the rope. What are the horizontal and vertical components of the force? 16. A student exerts a force of 72 N along the handle of a lawnmower to push it across the lawn. Find the horizontal and vertical components of this force when the handle is held at an angle with the lawn of: a. 60 degrees b. 40 degrees c. 30 degrees 17. Three people are pulling on a tree. The first person pulls with a 15 N force at 65 degrees; the second with 16 N at 135 degrees; the third with 11 N at 195 degrees. What is the magnitude of the resultant force on the tree? 18. Two forces act on an object. One force is 6.0 N horizontally. The second force is 8.0 N vertically. Find the magnitude of the resultant force. 19. Two forces act on an object. A 36 N force acts at 225 degrees. A 48 N force acts at 315 degrees. What would be the magnitude of the resultant force? Use the following diagram to answer questions 20 - 28 20. If side a and side b is 5, what is side c? What is angle x? 21. If side a is 15 and side b is 10, what is side c? What is angle x? 22. If side a is 5 and side b is 25, what is side c? What is angle x? 23. If side c is 25 and x is 30 degrees, what is side a? Side b? 24. If side c is 40 and x is 45 degrees, what is side a? Side b? 25. If side c is 100 and x is 65 degrees, what is side a? Side b? 26. If side b is 30 and x is 40 degrees, what is side a? Side c? 27. If side b is 30 and x is 60 degrees, what is side a? Side c? 28. If side b is 45 and x is 45 degrees, what is side a? Side c? 29. A boat is traveling across a river (at a 90 degree angle) at 20 m/s. If the river is moving 5 m/s, what is the new speed of the boat? 30. A boat is traveling across a river (at a 90 degree angle) at 15 m/s. If the river is moving the boat 4 m/s downstream at the same time, what is the actual speed of the boat? What angle is the boat actually moving? 31. A seal swims toward an inlet with a speed of 5.0 m/s as a current of 1.0 m/s flows in the opposite direction. How long will it take the seal to swim 100.0 m? (How fast is the seal actually moving?) 32. A pilot points a small plane north at 200 km./h. The wind speed is 40.0 km/h from the west blowing east. What is the actual velocity of the plane ? 33. While playing catch, Joe throws a ball at 30 m/s at 20 degrees above the horizontal. How fast is the ball initially moving up? How fast is the ball initially moving horizontally? 34. While laying siege to a fort, a cannon is pointed 30 degrees above the horizontal. If the cannon ball leaves the cannon with an initial speed of 200 m/s, what is the initial upward velocity? Horizontal velocity? 35. Some Antarctic explorers heading due south toward the pole travel 50 km during the first day. A sudden snow storm slows their progress and they move only 30 km the second day. With plenty of rest they travel the final 65 km the last day and reach the pole. What was the explorers’ displacement? 36. Lindsay and Hannah are out playing a game of tug o war. Lindsay can pull with a force of 45 N while Hannah can pull with a force of 60 N. a. Draw a vector diagram of the situation. b. Find the resultant force on the rope. 37. Tyler finds that when he drives his motor boat upstream he can travel with a speed of only 8 m/s, while he moves with a speed of 12 m/s when he heads downstream. What is the current of the river on which Tyler is traveling? 38. A plane travels at 200 km/h north while a strong wind pushes it east at 40 km/h. a. What is the plane’s resultant velocity? b. What is the direction? 39. A ball is thrown 40 m/s at 35 degrees from the horizontal? a. What is the vertical velocity component? b. What is the horizontal velocity component? 40. Jessica flies due east from San Francisco to Washington D. C., a displacement of 5600 km. She then flies from Washington to Boston, a displacement of 900 km at an angle of 55 degrees NE. What is Jessica’s total displacement?
