Additional Problems

| 51 | A chimpanzee sitting against his favorite tree gets up and walks 51 m due east and 39 m due south to reach a termite mound, where he eats lunch. (a) What is the shortest distance between the tree and the termite mound? (b) What angle does the shortest distance make with respect to due east?

| 52 | An observer, whose eyes are 1.83 m above the ground, is standing 32.0 m away from a tree. The ground is level, and the tree is growing perpendicular to it. The observer’s line of sight with the treetop makes an angle of 20.0° above the horizontal. How tall is the tree?

| 53 | ssm The speed of an object and the direction in which it moves constitute a vector quantity known as the velocity. An ostrich is running at a speed of 17.0 m/s in a direction of 68.0° north of west. What is the magnitude of the ostrich’s velocity component that is directed (a) due north and (b) due west?

| 54 | The variables x, v, and a have the dimensions of [L], [L]/[T], and [L]/[T]2, respectively. These variables are related by an equation that has the form , where n is an integer constant (1, 2, 3, etc.) without dimensions. What must be the value of n, so that both sides of the equation have the same dimensions? Explain your reasoning.

| 55 | You are on a treasure hunt and your map says “Walk due west for 52 paces, then walk 30.0° north of west for 42 paces, and finally walk due north for 25 paces.” What is the magnitude of the component of your displacement in the direction (a) due north and (b) due west?

| 56 | Displacement vector points due east and has a magnitude of 2.00 km. Displacement vector points due north and has a magnitude of 3.75 km. Displacement vector points due west and has a magnitude of 2.50 km. Displacement vector points due south and has a magnitude of 3.00 km. Find the magnitude and direction (relative to due west) of the resultant vector .

| 57 | ssm Two ropes are attached to a heavy box to pull it along the floor. One rope applies a force of 475 newtons in a direction due west; the other applies a force of 315 newtons in a direction due south. As we will see later in the text, force is a vector quantity. (a) How much force should be applied by a single rope, and (b) in what direction (relative to due west), if it is to accomplish the same effect as the two forces added together?

* | 58 | A force vector points at an angle of 52° above the axis. It has a y component of newtons. Find (a) the magnitude and (b) the x component of the force vector.

* | 59 | ssm Vector has a magnitude of 6.00 units and points due east. Vector points due north. (a) What is the magnitude of , if the vector points 60.0° north of east? (b) Find the magnitude of .

* | 60 | In wandering, a grizzly bear makes a displacement of 1563 m due west, followed by a displacement of 3348 m in a direction 32.0° north of west. What are (a) the magnitude and (b) the direction of the displacement needed for the bear to return to its starting point? Specify the direction relative to due east.

* | 61 | Before starting this problem, review Conceptual Example 7. The force vector has a magnitude of 90.0 newtons and points due east. The force vector has a magnitude of 135 newtons and points 75° north of east. Use the graphical method and find the magnitude and direction of (a) (give the direction with respect to due east) and (b) (give the direction with respect to due west).

* | 62 | You live in the building on the left in the drawing, and a friend lives in the other building. The two of you are having a discussion about the heights of the buildings, and your friend claims that his building is half again as tall as yours. To resolve the issue you climb to the roof of your building and estimate that your line of sight to the top edge of the other building makes an angle of 21° above the horizontal, while your line of sight to the base of the other building makes an angle of 52° below the horizontal. Determine the ratio of the height of the taller building to the height of the shorter building. State whether your friend is right or wrong.

** | 63 | What are the x and y components of the vector that must be added to the following three vectors, so that the sum of the four vectors is zero? Due east is the direction, and due north is the direction.

Copyright © 2007 John Wiley & Sons, Inc. All rights reserved.