Physics Test: Graphical Vectors Day 1

Multiple Choice

1. In a coordinate system, a vector is oriented at angle with respect to the x-axis. The x component of the vector equals the vector’s magnitude multiplied by which trigonometric function? A. cos  B. cot  C. sin  D. tan 

2. Use the diagram above. How many displacement vectors shown in the figure above have components that lie along the y-axis and are pointed in the –y direction? A. 3 B. 5 C. 2 D. 0 3. Use the diagram above. Which displacement vectors shown in the figure above have vertical components that are equal?

A. d and d B. d and d C. d and d D. d and d 4.Which of the following is the best coordinate system to analyze a car traveling northeast from one city to another? A. positive x-axis pointing west; positive y-axis pointing east B. positive x-axis pointing north; positive y-axis pointing south C. positive x-axis pointing east; positive y-axis pointing south D. positive x-axis pointing east; positive y-axis pointing north

5. In the figure above, which diagram represents the vector addition C = A + B? A. II B. III C. I D. IV 6. In the figure above, which diagram represents the vector subtraction C = A–B? A. IV B. I C. III D. II 7. Which of the following is a physical quantity that has a magnitude but no direction? A. vector C. scalar B. resultant D. frame of reference

8.Which of the following is the best coordinate system to analyze the movement of a submarine diving at an angle of 45° to the surface of the water? A. x-axis: up and down; y-axis: horizontal at the ocean bottom B. x-axis: horizontal at the water level; y-axis: up and down C. x-axis: left and right; y-axis: horizontal at the ocean bottom D. x-axis: horizontal at the water level; y-axis: left and right 9. Which of the following is the best coordinate system to analyze a painter climbing a ladder at an angle of 60° to the ground? A. x-axis: horizontal along the ground; y-axis: up and down B. x-axis: along the ladder; y-axis: horizontal along the ground C. x-axis: horizontal along the ground; y-axis: along the ladder D. x-axis: along the ladder; y-axis: up and down 10. Which of the following is the best coordinate system to analyze an object thrown into the air? A. x-axis: perpendicular to the ground; y-axis: up and down B. x-axis: up and down; y-axis: parallel to the ground C. x-axis: up and down; y-axis: perpendicular to the ground D. x-axis: parallel to the ground; y-axis: perpendicular to the ground 11. Which of the following is an example of a vector quantity? A. mass B. temperature C. velocity D. volume 12. Which of the following is a physical quantity that has both magnitude and direction? A. resultant C. scalar B. vector D. frame of reference 13. In a coordinate system, a vector is oriented at angle with respect to the x-axis. The y component of the vector equals the vector’s magnitude multiplied by which trigonometric function? A. cos  B. sin  C. tan  D. cot 

Short Answer

14. Briefly explain the triangle (or polygon) method of addition. 15. What is a resultant? 16. How can you use the Pythagorean theorem to add two vectors that are not perpendicular?

Problem

17. A cave explorer travels 3.0 m eastward, then 2.5 m northward, and finally 15.0 m westward. Use the graphical method to find the magnitude of the net displacement. 18. A vector has magnitude 58.0 units and is inclined to the positive axis of x at 42.0°. Vector has magnitude 36.0 units and is inclined to the positive axis of x at 121°. Vector has magnitude 40.0 units and is inclined to the positive axis of x at 53.0°. Use the graphical method to find the resultant of the vectors , , and . Physics Test: Graphical Vectors Day 2

Problem

19. June starts out hiking due south and travels 4.50 km. When she comes to a canyon running east to west, she turns due east and travels 12.0 km before stopping for the night. a. How far did she travel this first day? Draw the vectors of the distances walked. b. The next day, June consults her map and sets out on a path 35.0° south of due east, hiking 7.75 km before coming to a river flowing from north to south. She turns due south and follows the river for 11.0 km, and again she stops for the night. How far did she travel this second day? Draw the vectors of the distances walked. c. After two days of hiking, how far is June from her original starting point? 20. A jogger runs 10.0 blocks due east, 5.0 blocks due south, and another 2.0 blocks due east. Assume all blocks are of equal size. Use the graphical method to find the magnitude of the jogger’s net displacement. 21. A dog walks 28 steps north and then walks 55 steps west to bury a bone. If the dog walks back to the starting point in a straight line, how many steps will the dog take? Use the graphical method to find the magnitude of the net displacement.

22. Use the diagram below. The magnitude of the force is 57 N, of force is 57 N, and of is 57 N. The angles and are 30° each. Use the graphical method to find the resultant of the forces , , and .

23. A wooden block of 20.0 kg rests on a horizontal wooden plank. The plank is lifted by one end until it forms a 40.0° angle with the floor. Draw a diagram of the forces acting on this block as it is positioned.