Multiple-Concept Example 9 reviews the concepts that play a role in this problem. Two forces are applied to a tree stump to pull it out of the ground. Force F_A(vector) has a magnitude of 2240 newtons and points 34.0° south of east, while force F_B(vector) has a magnitude of 3160 newtons and points due south. Using the component method, find the magnitude and direction of the resultant force F_A(vector) + F_B(vector) that is applied to the stump. Specify the direction with respect to due east.

Concept Example 9

A jogger runs 145 m in a direction 20.0° east of north (displacement vector A_(vector)) and then 105 m in a direction 35.0° south of east (displacement vector B_(vector)). Using components, determine the magnitude and direction of the resultant vector C_(vector) for these two displacements.

Reasoning Figure 1.22 shows the vectors A_(vector) and B_(vector), assuming that the y axis corresponds to the direction due north. The vectors are arranged in a tail-to-head fashion, with the resultant vector C_(vector) drawn from the tail of A_(vector) to the head of B_(vector). The components of the vectors are also shown in the fi gure. Since C_(vector) and its components form a right triangle (red in the drawing), we will use the Pythagorean theorem and trigonometry to express the magnitude and directional angle θ for C_(vector) in terms of its components. The components of C_(vector) will then be obtained from the components of A_(vector) and B_(vector) and the data given for these two vectors.

Knowns and Unknowns The data for this problem are listed in the table that follows:

Description Symbol Value Comment Magnitude of vector A 145 m Direction of vector 20.0 east of north See Figure 1.22. Magnitude of vector B 105 m Direction of vector B 35.0 south of east See Figure 1.22. Unknown Variable Magnitude of resultant vector C Direction of resultant vector ?