6. Three displacement vectors of a croquet ball are shown in the figure below, where |Ã| m, |B| = 40.0 m, |Č| = = 20.0 30.0 m. Find (a) the resultant in unit-vector notation and (b) the magnitude and direction of the resultant displacement. Express the direction in terms of the angle relative to the positive x axis. y B 45.0° x 45.0°

Vector A has a magnitude of 4.50 m and makes an angle of 64.0 with the positive x axis. Vector B, with a magnitude equal to that of vector A, points along the negative y axis (Fig. P3.16). Graphically find the magnitude and direction of the resultant vector a. A+B, b. AB, c. BA, and d. 2AB.

Three displacement vectors of a croquet ball are shown in Figure P1.44, where |A|=20.0units, |B|=40.0units, and |C|=30.0units. Find (a) the resultant in unit-vector notation and (b) the magnitude and direction of the resultant displacement. Figure P1.44

What is the y component of the vector shown in Figure OQ3.9? (a) 3 cm (b) 6 cm (c) 4 cm (d) 6 cm (e) none of those answers

A vector points from the origin into the second quadrant of the xy plane. What can you conclude about its components? (a) Both components are positive. (b) The x component is positive, and the y component is negative. (c) The x component is negative, and the y component is positive. (d) Both components are negative. (e) More than one answer is possible.

A skater glides along a circular path of radius 5.00 m in clockwise direction. ‘When he coasts around one- half of the circle, starting from the west point, find (a) the magnitude of his displacement vector and (b) how far he actually skated. (c) What is the magnitude of his displacement vector when he skates all the way around the circle and comes back to the west point?

The resultant vector R=2AB2C has zero magnitude. Vector A has an x component of 4.60 m and a y component of 12.1 m. and vector B has an x component of 3.00 m and a y component of 4.00 m. What are the x and y components of vector C? (All of these are two-dimensional vectors.)

Assuming the +x-axis is horizontal to the right for the vectors in the preceding figure, find (a) the component of vector Aalong vector C , (b) the component of vector Calong vector A , (c) the component of vector i along vector F , and (d) the component of vector Falong vector i .

The displacement vectors 42.0 cm at 15.0 and 23.0 cm at 65.0 both start from the origin and form two sides of a parallelogram. Both angles are measured counterclockwise from the x axis. (a) Find the area of the parallelogram. (b) Find the length of its longer diagonal.

A surveyor measures the distance across a straight river by the following method (Fig. P3.7). Starting directly across from a tree on the opposite bank, she walks d = 100 m along the riverbank to establish a baseline. Then she sights across to the tree. The angle from her baseline to the tree is = 35.0. How wide is the river?