Worksheet to Review Vector and Scalar Properties

Transcription

1 Worksheet to Review Vector and Scalar Properties 1. Differentiate between vectors and scalar quantities 2. Know what is being requested when the question asks for the magnitude of a quantity 3. Define what is meant by stating a vector in polar notation 4. Define what is meant by stating a vector i,j notation 5. Be able to convert from polar to I,j and vice versa 6. Differentiate between reference angles and directional angles 7. Differentiate between concurrent vectors and sequential vectors 8. Differentiate between distance and displacement 9. Differentiate between average speed and average velocity 10. State and be able to use the Pythagorean Theorem. 11. Know the trig ratios for sine, cosine, and tangent within a right triangle 12. Be able to add vectors graphically by the parallelogram method and by head to tail 13. Be able to write resultant vector equations for a given vector diagram I. Label the missing angles and lengths of each side in the following right triangles II. Carefully construct the resultant of each set of the following concurrent vectors

2 III. Using a scaled diagram and the head to tail method, graphically determine the magnitude and direction of the resultant vector of the following sequential vectors. (5 cm, 37º) then (6 cm, 90º) then (4 cm, 210º) and then (7 cm, 270º) IV. Sketch each of the following vectors and then calculate their reference angle and directional angle. A = 3i + 4j B = 4i 3j C = 3i + 4j D = 4i 3j State the polar coordinates for vectors A, B, C, and D. A = (, ) C = (, ) B = (, ) D = (, )

3 V. Calculate the x and y components for the following 4 vectors. State your answers as decimals in I,j notation. E = (10 cm, 30 degrees) F = (8 cm, 135 degrees) G = (12 cm, 240 degrees) H = (6 cm, 307 degrees) VI. Use the trig table provided (not your calculators) to determine the following angles. tan ( ) = tan ( ) = tan ( ) = tan ( ) = tan ( ) = tan ( ) = VII. Calculate the average speed of a cart in m/sec if it travels at 5 m/sec for 8 minutes and then 2 minutes at 3 m/sec. VIII. Calculate the magnitudes of a jogger s average velocity and average speed in m/sec if he completes 2.5 laps around a track having a circumference of 100 meters and a diameter of 32 meters in 3 minutes.

4 IX. At 10:30 on Sept 15 th, 2012, a student measures his shadow to be 180 cm long. If the angle of the sun s altitude was 42.0 degrees, then how tall was the student? If a second student had a shadow at the exact same time that was 155 cm long, how tall was that student? X. A gigantic fountain of water is in the center of a circular pool of water. If you walk around the circumference of the pool, it is a distance of 74 meters. If you then sit on the edge of the pool, using a protractor you can gauge the angle of elevation to the top of the fountain to be 55 degrees. How high is the fountain? XI. Complete these vector equations based on the following diagram. B + E = A + C =

5 XII. The following data was taken during our spring scale lab. Use a protractor and a centimeter ruler to measure the x and y components of the vectors shown below. (Diagram is NOT drawn to scale) Vector Reading x component y component Longest 10 N 10 0 Middle sized 8.8 N Shortest 8.0 N Was the washer in equilibrium? Support your answer. XIII. Calculate the length of the unknown side, a, and then determine the unknown angle, A. a =? A =?

6 XIV. Algebraically determine the magnitude and direction of the net displacement for the following steps. Show your x y chart, your values for net x and net y, your vector diagram of net x and net y to obtain R, labeling your reference angle, directional angle, and R s magnitude. (5 m, 90º) then (5 m, 180º) then (10 m, 233º) and finally (4 m, 330º) XV. Multiple Choice examples Army engineers in 1946 determined the distance from the Earth to the moon by using radar. If the time from which a signal was sent out from their radar to the time at which it was received back was 2.56 s, what is the distance from the Earth to the moon? (The speed of radar waves is 3 x 10 8 m/s). a. 480,000 km b. 768,000 km c. 240,000 km d. 384,000 km If a jet airplane climbs at an angle of 15 with respect to the horizontal and follows a straight-line path for a distance of 400 m, how much altitude did it gain? a. 200 m b. 141 m c. 103 m d. 390 m

7 A railroad train travels forward along a straight track at 80 m/s for 1000 m and then travels at 50 m/s for the next 1000 m. What is the average velocity? a m/s b m/s c m/s d m/s An initial displacement of 6 m is followed by a second displacement of 3 m. Which net displacement is impossible to achieve? a. 6 m b. 3 m c. 2 m d. 9 m A jogger runs two complete laps around a circular path having a radius of 60 m. What was his net displacement and total distance? a. 120 m, 377 m b. 120 m, 754 m c. 377 m, 377 m d. 0 m, 754 m An ant on a picnic table travels 30 cm eastward, then 25 cm northward and finally 15 cm westward. What is its directional displacement with respect to its original position? a. 77 b. 29 c. 141 d. 59 What is the magnitude of the ant s net displacement? a. 52 cm b. 70 cm c. 57 cm d. 29 cm

8 If the ant took 10 seconds to complete its trip, what was its average speed? a. 1.0 cm/sec b. 7.0 cm/sec c. 5.7 cm/sec d. 2.9 cm/sec Vector A is 3 units in length and points along the positive x-axis; vector B is 4 units in length and points along a direction 150 from the positive x-axis. What is the magnitude of the resultant when vectors A and B are added? a. 2.1 b. 6.7 c. 4.7 d. 7.0 Vector A is 3 units in length and points along the positive x-axis; vector B is 4 units in length and points along a direction 150 from the positive x-axis. What is the direction of the resultant with respect to the positive x-axis? a. 13 b. 86 c. 103 d. 77 Vector S = (10, 37º), vector T = (8, 90º), and vector U = (6, 180º). What is the magnitude of the vector R = S T + ½U? a. 0.4 b. 5.4 c d. 3.0