Free Response Problem1. A bus makes three displacements in the following order:1) 38 mi, 48 east of north2) 79 mi, 46 west of north; and3) 55 mi, south-easta. Draw a clear diagram showing all three displacement vectors with respect to horizontal points (north, east, south, and west).

b. Find the X and Y components of displacement D1.

c. Find the X and Y components of displacement D2.

d. Find the X and Y components of displacement D3.

e. Find the magnitude of the resultant vector.

f. Find the direction of the resultant vector.

2. A man riding his bicycle travels in the following order:1) 15 mi, 30 west of south2) 12 mi, 65 west of north; and3) 8 mi easta. Draw a clear diagram showing all three displacement vectors with respect to the north, south, east and west.

b. Find the X and Y components of displacement D1.

c. Find the X and Y components of Displacement D2.

d. Find the X and Y components of displacement D3.

e. Find the magnitude of the resulting vector.

f. Determine the direction of the resulting vector.

3. A car makes three displacements on the way to the bank. These displacements are then displayed on a graph. Their components are as follows:1) D1= (28.8, 18)2) D2= (-4.5, -25.6)3) D3= (10.6, -5.6)

a. Find the magnitude and the measure of the angle formed by D1.

b. Find the magnitude and the measure of the angle formed by D2.

c. Find the magnitude and the measure of the angle formed by D3.

d. Plot all three vectors on a graph with respect to the x and y coordinates.

e. Determine the magnitude of the resultant vector.

f. Find the angled formed by the resultant vector.

4. Two vectors are presented by the diagram above.a. Write vector in terms of unit vectors and .b. Write vector in terms of unit vectors and .c. Use unit vectors to express the vector =2 +3d. Use unit vectors to express the vector =5 -6

5. Two vectors are given in terms of unit vectors = 5 + 2, = 4 -3.a. Find the magnitude of vector .b. Find the magnitude of vector .c. Write an expression for the vector difference - using unit vectors.d. Find the magnitude of the vector difference.e. Find the direction of the vector difference.

6. Three vectors are presented by the diagram above.a. Find the scalar product of two vectors b. Find the scalar product of two vectors c. Find the scalar product of two vectors

7. Three vectors are presented by the diagram above.a. Find the scalar product of two vectors b. Find the scalar product of two vectors c. Find the scalar product of two vectors

8. Find the angle between each of the following pairs of vectors.a. = -3 +5 and = 4 -2b. = 4 +6 and = 8 +5c. = -5 +3 and = 8 +12d. = -12 -8 and = 10 +6

9. Three vectors are presented by the diagram above.a. Find the magnitude and the direction of the vector product b. Find the magnitude and the direction of the vector product c. Find the magnitude and the direction of the vector product

10. Three vectors are presented by the diagram above.a. Find the magnitude and the direction of the vector product b. Find the magnitude and the direction of the vector product c. Find the magnitude and the direction of the vector product Answer Key:79 mi

1. A. 464845

38 mi

55 mi

B. = 28.3 = 25.64

C. = -56.82 = 54.87

D. = -38.9 = -38.9

E. 42.71 mi

F. 75.9

2. A. 12 mi

658 mi

30

15 mi

B. = -7.5 = -13

C. = -10.9 = 5.07

D. = 8 = 0

E. 13.1 mi

F. 217.2

3. A. 33.97, 32B. 26, 260C. 12, 332.2D. 33.97

1227.8102632

E. 37.17F. 339.3

4. A. = -1.44 + 1.92B. = 3 - 1.1C. = 6.12 + 0.54D. = -25.2 + 16.2

5. A. 5.39B. 5C. + 5D. 5.1E. 78.69

6. A. 0B. -90.21C. -43.76 7. A. 0B. -154.73C. -414.23

8. A. 147.6B. 24.23C. 92.77D. 177.69

9. A. 224m, -z directionB. 38.29m, -z directionC. 103.1m, -z direction

10. A. 550, -z directionB. 364.52, -z directionC. 175.83, -z direction