Vectors and Vector Addition

Problems for solution without assistance

Problem 1

Compute the x- and y-components of each vector:
a) 12m 37° clockwise from the y-axis.
b) 15m —40°;
c) 6.0 m 60° counterclockwise from the -x-axis.

Problem 2

Find the magnitude and direction of the vector represented by each of the following pairs of components:
a)A_x = 5.60cm, A_y = -8.20cm;
b) Ax = -2.70m, A_y - 9.45m;
c) A_x = -3.75km, A_y = 6.70km

Problem 3

Vector A has components A_x = 3.40cm, A_y = 2.25cm; vector B has the components B_x = — 4.10cm, B_y = 3.75cm. Find
a) the components of the vector sum A + B;
b) the magnitude and direction of the vector sum;
c) the components of the vector difference A - B;
d) the magnitude and direction of the vector difference

Problem 4

A disoriented physics professor drives 4.25 km south, then 2.75 km west, then 1.50 km north. Find the Magnitude and Direction of the resultant displacement, using the method of components.

Problem 5

Vector A is 2.80 cm long and is 60° above the +x-axis. Vector B is 1.90 cm long and is 60° below the x-axis in the forth quadrant. Find the magnitude and direction of
a) A + B;
b) A - B;
c) B - A

Problem 6

Given two vectors 5i + 2j and B = 3i - lj, find the magnitude of each vector;
b) write an expression for the vector difference A - B, using unit vectors;
c) find the magnitude and direction for the vector difference.

Problem 7

Find the Scalar Product of A * B for the vectors: A = -12i, B = 14.4i + 10.8j .

Problem 8

For the two vectors in Problem 7.
a) Find the magnitude and direction of the vector product A x B;
b) find the magnitude and direction of the vector product B x A.

Problem 9

You are to program a robotic arm on an assembly line to move in the xy-plane. Its first displacement is A; its second displacement is B of magnitude 4.80 cm and direction 49° measured clockwise from the +x-axis. The resultant C = A + B of the two displacements should have a magnitude of 4.80 cm but a direction 22.0° counterclockwise from the +x-axis.
a) Find the components of A.
c) Find the magnitude and direction of A.

Problem 10

An explorer in the dense jungles of equatorial Africa leaves her hut. She takes 80 steps southeast, the 40 step 60° east of north, then 50 steps due north. Assume her steps all have equal length,
a) Save her from becoming hopelessly lost in the jungle by giving her the displacement vector that will lead her back to her hut.

Examples of solutions

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