A person is jogging along a straight line, and her

The highest waterfall in the world is Angel Falls in Venezuela, with a total drop of 979.0 m (see Figure 1.4). Express this drop in feet.

Express the speed limit of 65 miles/hour in terms of meters/second.

The body mass index (BMI) takes into account your mass in kilograms (kg) and your height in meters (m) and is defined as follows:However, the BMI is often computed using the weight* of a person in pounds (lb) and his or her height in inches (in.). Thus, the expression for the BMI incorporates these quantities, ratherthan the mass in kilograms and the height in meters. Starting with the definition above, deter- mine the expression for the BMI that uses pounds and inches.

(a) Is it possible for two quantities to have the same dimensions but different units? (b) Is it possible for two quantities to have the same units but different dimensions?

You can always add two numbers that have the same units (such as 6 meters 3 meters). Can you always add two numbers that have the same dimensions, such as two numbers that have the dimensions of length [L]?

The following table lists four variables, along with their units:These variables appear in the following equations, along with a few numbers that have no units. In which of the equations are the units on the left side of the equals sign consistent with the units on the right side?

In the equation y cn at 2 you wish to determine the integer value (1, 2, etc.) of the exponent n.The dimensions of y, a, and t are known. It is also known that c has no dimensions. Can dimen- sional analysis be used to determine n?

On a sunny day, a tall building casts a shadow that is 67.2 m long. The angle between the suns rays and the ground is 50.0, as Figure 1.6 shows. Determine the height of the building.

A lakefront drops off gradually at an angle , as Figure 1.7 indicates. For safety reasons, it is necessary to know how deep the lake is at various distances from the shore. To provide some information about the depth, a lifeguard rows straight out from the shore a distance of 14.0 m and drops a weighted fishing line. By measuring the length of the line, the lifeguard determines the depth to be 2.25 m. (a) What is the value of ? (b) What would be the depth d of the lake at a distance of 22.0 m from the shore?

There are places where the temperature is 20 C at one time of the year and 20 C at another time. Do the plus and minus signs that signify positive and negative temperatures imply that temperature is a vector quantity? (a) Yes (b) No R

Consider two vectors described as follows: 1. A woman climbs 1.2 m up a ladder, so that her displacement vector is 1.2 m, upward along the ladder, as in Figure 1.12a. 2. A man is pushing with 450 N of force on his stalled car, trying to move it eastward. The force vector that he applies to the car is 450 N, due east, as in Figure 1.13a. What are the physical meanings of the vectors  and  ? (a)  points upward along the ladder and has a magnitude of 1.2 m;  points due east and has a magnitude of 450 N. (b)  points downward along the ladder and has a magnitude of 1.2 m;  points due west and has a magnitude of 450 N. (c)  points downward along the ladder and has a magnitude of 1.2 m;  points due west and has a magnitude of 450 N. Rea

A displacement vector has a magnitude of r 175 m and points at an angle of 50.0 relative to the x axis in Figure 1.20. Find the x and y components of this vector.

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

Figure 1.24 shows two displacement vectors and . Vector points at an angle of 22.0 above the x axis and has an unknown magnitude. Vector has an x component Bx 35.0 m and has an unknown y component By. These two vectors are equal. Find the magnitude of and the value of By.

What does the fact that vector equals vector imply about the magnitudes and directions of the vectors?

Figure 1.25 shows three displacement vectors , , and . These vectors are arranged in tailto-head fashion, because they add together to give a resultant displacement , which lies along the x axis. Note that the vector is parallel to the x axis. What is the magnitude of the vector and its directional angle ?

How is the magnitude of related to its scalar components Ax and Ay? Answer The magnitude of is given by the Pythagorean theorem in the form , since a vector and its components form a right triangle (see Figure 1.26). Do any of the vectors in Figure 1.25 have a zero value for either their x or y components? Answer Yes. The vectors and each have a zero value for their y component. This is because these vectors are parallel to the x axis. What does the fact that , , and add together to give the resultant tell you about the components of these vectors? Answer The fact that means that the sum of the x components of , , and equals the x component of (Ax Bx Cx Rx) and the sum of the y components of , , and equals the y component of (Ay By Cy Ry). Solut

During a relay race, runner A runs a certain distance due north and then hands off the baton to runner B, who runs for the same distance in a direction south of east. The two displacement vectors and can be added together to give a resultant vector . Which drawing correctly shows the resultant vector? (a) 1 (b) 2 (c) 3 (d) 4

How is the magnitude R of the resultant vector in the drawing related to the magnitudes A and B of the vectors and ? (a) The magnitude of the resultant vector is equal to the sum of the magnitudes of and , or R  A  B. (b) The magnitude of the resultant vector is greater than the sum of the magnitudes of and , or R A  B. (c) The magnitude of the resultant vector is less than the sum of the magnitudes of and , or R A  B.

The first drawing shows three displacement vectors, , , and , which are added in a tail-to-head fashion. The resultant vector is labeled . Which of the following drawings shows the correct resultant vector for ? A (a) 1 (b) 2 (c) 3

The first drawing shows the sum of three displacement vectors, , , and . The resultant vector is labeled . Which of the following drawings shows the correct resultant vector for A ? (a) 1 (b) 2 (c) 3

A person is jogging along a straight line, and her displacement is denoted by the vector in the drawings. Which drawing represents the correct vector components, x and y, for the vector ? A (a) 1 (b) 2 (c) 3 (d) 4

A person drives a car for a distance of 450.0 m. The displacement of the car is illustrated in the drawing. What are the scalar components of this displacement vector? (a) Ax  0 m and Ay  450.0 m (b) Ax  0 m and Ay  450.0 m (c) Ax  450.0 m and Ay  450.0 m (d) Ax  450.0 m and Ay  0 m (e) Ax  450.0 m and Ay  450.0 m A

Drawing a shows a displacement vector (450.0 m along the y axis). In this x, y coordinate system the scalar components are Ax  0 m and Ay  450.0 m. Suppose that the coordinate system is rotated counterclockwise by 35.0, but the magnitude (450.0 m) and direction of vector remain unchanged, as in drawing b. What are the scalar components, Ax and Ay, of the vector in the rotated x, y coordinate system? (a) Ax  369 m and Ay  258 m (b) Ax  369 m and Ay  258 m (c) Ax  258 m and Ay  369 m (d) Ax  258 m and Ay  369 m (e) Ax  258 m and Ay  369 m A B A

Suppose the vectors and in the drawing have magnitudes of 6.0 m and are directed as shown. What are Ax and Bx, the scalar components of and along the B x axis? B A B B B A B +y +x +x +y (1) Ax Ay Ay Ax A (2) A Ax Bx (a) (6.0 m) cos 354.9 m (6.0 m) cos 354.9 m (b) (6.0 m) sin 353.4 m (6.0 m) cos 354.9 m (c) (6.0 m) cos 354.9 m (6.0 m) sin 353.4 m (d) (6.0 m) cos 354.9 m (6.0 m) cos 354.9 m (e) (6.0 m) sin 353.4 m (6.0 m) sin 353.4 m Continued A B 35

Drawing a shows two vectors and , and drawing b shows their components. The scalar components of these vectors are as follows: When the vectors and are added, the resultant vector is , so that . What are the values of Rx and Ry, the x and y components of ?

The displacement vectors and , when added together, give the resultant vector , so that . Use the data in the drawing to find the magnitude R of the resultant vector and the angle that it makes with the x axis. R

A student sees a newspaper ad for an apartment that has 1330 square feet (ft 2 ) of floor space. How many square meters of area are there?

Bicyclists in the Tour de France reach speeds of 34.0 miles per hour (mi/h) on flat sections of the road. What is this speed in (a) kilometers per hour (km/h) and (b) meters per second (m/s)?

Vesna Vulovic survived the longest fall on record without a parachute when her plane exploded and she fell 6 miles, 551 yards. What is this distance in meters?

Suppose a mans scalp hair grows at a rate of 0.35 mm per day. What is this growth rate in feet per century?

Given the quantities a 9.7 m, b 4.2 s, c 69 m/s, what is the value of the quantity d a3 /(cb2 )? 6.

Consider the equation . The dimensions of the variables v, x, and t are [L]/[T], [L], and [T], respectively. The numerical factor 3 is v 1 3 zxt 2 A B R +y 6.0 m 8.0 m 23 +x +y +x A B 35 35 6.0 m 6.0 m (a) dimensionless. What must be the dimensions of the variable z, such that both sides of the equation have the same dimensions? Show how you determined your answer.

A bottle of wine known as a magnum contains a volume of 1.5 liters. A bottle known as a jeroboam contains 0.792 U.S. gallons. How many magnums are there in one jeroboam?

The CGS unit for measuring the viscosity of a liquid is the poise (P): 1 P 1 g/(s  cm). The SI unit for viscosity is the kg/(s  m). The viscosity of water at 0 C is 1.78  103 kg/(s  m). Express this viscosity in poise.

Azelastine hydrochloride is an antihistamine nasal spray. A standard-size container holds one fluid ounce (oz) of the liquid. You are searching for this medication in a European drugstore and are asked how many milliliters (mL) there are in one fluid ounce. Using the following conversion factors, determine the number of milliliters in a volume of one fluid ounce: 1 gallon (gal) 128 oz, 3.785  103 cubic meters (m3 ) 1 gal, and 1 mL 106 m3 . *

A partly full paint can has 0.67 U.S. gallons of paint left in it. (a) What is the volume of the paint in cubic meters? (b) If all the remaining paint is used to coat a wall evenly (wall area 13 m2 ), how thick is the layer of wet paint? Give your answer in meters.

A spring is hanging down from the ceiling, and an object of mass m is attached to the free end. The object is pulled down, thereby stretching the spring, and then released. The object oscillates up and down, and the time T required for one complete up-and-down oscillation is given by the equation where k is known as the spring constant. What must be the dimension of k for this equation to be dimensionally correct?

You are driving into St. Louis, Missouri, and in the distance you see the famous Gateway-to-the-West arch. This monument rises to a height of 192 m. You estimate your line of sight with the top of the arch to be 2.0 above the horizontal. Approximately how far (in kilometers) are you from the base of the arch?

A highway is to be built between two towns, one of which lies 35.0 km south and 72.0 km west of the other. What is the shortest length of highway that can be built between the two towns, and at what angle would this highway be directed with respect to due west?

A hill that has a 12.0% grade is one that rises 12.0 m vertically for every 100.0 m of distance in the horizontal direction. At what angle is such a hill inclined above the horizontal?

The corners of a square lie on a circle of diameter D  0.35 m. Each side of the square has a length L. Find L

The drawing shows a person looking at a building on top of which an antenna is mounted. The horizontal distance between the persons eyes and the building is 85.0 m. In part a the person is looking at the base of the antenna, and his line of sight makes an angle of 35.0 with the horizontal. In part b the person is looking at the top of the antenna, and his line of sight makes an angle of 38.0 with the horizontal. How tall is the antenna?

The two hot-air balloons in the drawing are 48.2 and 61.0 m above the ground. A person in the left balloon observes that the right balloon is 13.3 above the horizontal. What is the horizontal distance x between the two balloons?

What is the value of each of the angles of a triangle whose sides are 95, 150, and 190 cm in length? (Hint: Consider using the law of cosines given in Appendix E.)

The drawing shows sodium and chloride ions positioned at the corners of a cube that is part of the crystal structure of sodium chloride (common table salt). The edges of the cube are each 0.281 nm (1 nm  1 nanometer  109 m) in length. What is the value of the angle in the drawing? C

A person is standing at the edge of the water and looking out at the ocean (see the drawing). The height of the persons eyes above the water is h  1.6 m, and the radius of the earth is R  6.38 106 m. (a) How far is it to the horizon? In other words, what is the distance d from the persons eyes to the horizon? (Note: At the horizon the angle between the line of sight and the radius of the earth is 90.) (b) Express this distance in miles.

Three deer, A, B, and C, are grazing in a field. Deer B is located 62 m from deer A at an angle of 51 north of west. Deer C is located 77 north of east relative to deer A. The distance between deer B and C is 95 m. What is the distance between deer A and C? (Hint: Consider the law of cosines given in Appendix E.) *

An aerialist on a high platform holds on to a trapeze attached to a support by an 8.0-m cord. (See the drawing.) Just before he jumps off the platform, the cord makes an angle of 41 with the vertical. He jumps, swings down, then back up, releasing the trapeze at the instant it is 0.75 m below its initial height. Calculate the angle that the trapeze cord makes with the vertical at this instant.

(a) Two workers are trying to move a heavy crate. One pushes on the crate with a force , which has a magnitude of 445 newtons and is directed due west. The other pushes with a force , which has a magnitude of 325 newtons and is directed due north. What are the magnitude and direction of the resultant force applied to the crate? (b) Suppose that the second worker applies a force instead of . What then are the magnitude and direction of the resultant force applied to the crate? In both cases express the direction relative to due west.

A force vector points due east and has a magnitude of 200 newtons. A second force is added to . The resultant of the two vectors has a magnitude of 400 newtons and points along the east/west line. Find the magnitude and direction of . Note that there are two answers.

Consider the following four force vectors: Which two vectors add together to give a resultant with the smallest magnitude, and which two vectors add to give a resultant with the largest magnitude? In each case specify the magnitude and direction of the resultant.

Vector has a magnitude of 63 units and points due west, while vector has the same magnitude and points due south. Find the magnitude and direction of (a) and (b) . Specify the directions relative to due west.

Two bicyclists, starting at the same place, are riding toward the same campground by two different routes. One cyclist rides 1080 m due east and then turns due north and travels another 1430 m before reaching the campground. The second cyclist starts out by heading due north for 1950 m and then turns and heads directly toward the campground. (a) At the turning point, how far is the second cyclist from the campground? (b) In what direction (measured relative to due east) must the second cyclist head during the last part of the trip?

The drawing shows a triple jump on a checkerboard, starting at the center of square A and ending on the center of square B. Each side of a square measures 4.0 cm. What is the magnitude of the displacement of the colored checker during the triple jump?

Given the vectors and shown on the grid, sketch and calculate the magnitudes of the vectors (a) and (b) Use the tail-to-head method and express the magnitudes in centimeters with the aid of the grid scale shown in the drawing.

Vector has a magnitude of 12.3 units and points due west. Vector points due north. (a) What is the magnitude of if has a magnitude of 15.0 units? (b) What is the direction of relative to due west? (c) What is the magnitude of if has a magnitude of 15.0 units? (d) What is the direction of relative to due west?

A car is being pulled out of the mud by two forces that are applied by the two ropes shown in the drawing. The dashed line in the drawing bisects the 30.0 angle. The magnitude of the force applied by each rope is 2900 newtons. Arrange the force vectors tail to head and use the graphical technique to answer the following questions. (a) How much force would a single rope need to apply to accomplish the same effect as the two forces added together? (b) How would the single rope be directed relative to the dashed line?

A jogger travels a route that has two parts. The first is a displacement of 2.50 km due south, and the second involves a displacement that points due east. (a) The resultant displacement has a magnitude of 3.75 km. What is the magnitude of , and what is the direction of relative to due south? (b) Suppose that had a magnitude of 3.75 km. What then would be the magnitude of , and what is the direction of relative to due south?

At a picnic, there is a contest in which hoses are used to shoot water at a beach ball from three directions. As a result, three forces act on the ball, , , and (see the drawing). The magnitudes of and are F1 50.0 newtons and F2 90.0 newtons. Using a scale drawing and the graphical technique, determine (a) the magnitude of and (b) the angle such that the resultant force acting on the ball is zero.

A force vector has a magnitude of 575 newtons and points at an angle of 36.0 below the positive x axis. What are (a) the x scalar component and (b) the y scalar component of the vector?

Vector points along the y axis and has a magnitude of 100.0 units. Vector points at an angle of 60.0 above the x axis and has a magnitude of 200.0 units. Vector points along the x axis and has a magnitude of 150.0 units. Which vector has (a) the largest x component and (b) the largest y component? 36. Soccer player #1 is 8.6 m from the goal (see the drawing). If she kicks the ball directly into the net, the ball has a displacement labeled . If, on the other hand, she first kicks it to player #2, who then kicks it into the net, the ball undergoes two successive displacements, y and x. What are the magnitudes and directions of x and y? 37.

The components of vector are Ax and Ay (both positive), and the angle that it makes with respect to the positive x axis is . Find the angle if the components of the displacement vector are (a) Ax 12 m and Ay 12 m, (b) Ax 17 m and Ay 12 m, and (c) Ax 12 m and Ay  17 m.

During takeoff, an airplane climbs with a speed of 180 m/s at an angle of 34 above the horizontal. The speed and direction of the airplane constitute a vector quantity known as the velocity. The sun is shining directly overhead. How fast is the shadow of the plane moving along the ground? (That is, what is the magnitude of the horizontal component of the planes velocity?)

The x vector component of a displacement vector has a magnitude of 125 m and points along the negative x axis. The y vector component has a magnitude of 184 m and points along the negative y axis. Find the magnitude and direction of Specify the direction with respect to the negative x axis.

Your friend has slipped and fallen. To help her up, you pull with a force , as the drawing shows. The vertical component of this force is 130 newtons, and the horizontal component is 150 newtons. Find (a) the magnitude of and (b) the angle .

The displacement vector has scalar components of Ax 80.0 m and Ay 60.0 m. The displacement vector has a scalar component of Bx 60.0 m and a magnitude of B 75.0 m. The displacement vector has a magnitude of C 100.0 m and is directed at an angle of 36.9 above the x axis. Two of these vectors are equal. Determine which two, and support your choice with a calculation. * 42

Two racing boats set out from the same dock and speed away at the same constant speed of 101 km/h for half an hour (0.500 h), the blue boat headed south of west, and the green boat headed south of west. During this half hour (a) how much farther west does the blue boat travel, compared to the green boat, and (b) how much farther south does the green boat travel, compared to the blue boat? Express your answers in km.

The magnitude of the force vector is 82.3 newtons. The x component of this vector is directed along the x axis and has a magnitude of 74.6 newtons. The y component points along the y axis. (a) Find the direction of relative to the x axis. (b) Find the component of along the y axis.

The drawing shows a force vector that has a magnitude of 475 newtons. Find the (a) x, (b) y, and (c) z components of the vector.

Consult Multiple-Concept Example 9 in preparation for this problem. A golfer, putting on a green, requires three strokes to hole the ball. During the first putt, the ball rolls 5.0 m due east. For the second putt, the ball travels 2.1 m at an angle of 20.0 north of east. The third putt is 0.50 m due north. What displacement (magnitude and direction relative to due east) would have been needed to hole the ball on the very first putt?

The three displacement vectors in the drawing have magnitudes of A 5.00 m, B 5.00 m, and C 4.00 m. Find the resultant (magnitude and directional angle) of the three vectors by means of the component method. Express the directional angle as an angle above the positive or negative x axis. 47

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 has a magnitude of 2240 newtons and points 34.0 south of east, while force has a magnitude of 3160 newtons and points due south. Using the component method, find the magnitude and direction of the resultant force that is applied to the stump. Specify the direction with respect to due east.

A baby elephant is stuck in a mud hole. To help pull it out, game keepers use a rope to apply a force , as part a of the drawing shows. By itself, however, force is insufficient. Therefore, two additional forces and are applied, as in part b of the drawing. Each of these additional forces has the same magnitude F. The magnitude of the resultant force acting on the elephant in part b of the drawing is k times larger than that in part a. Find the ratio F/FA when k 2.00.

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

Multiple-Concept Example 9 provides background pertinent to this problem. The magnitudes of the four displacement vectors shown in the drawing are A 16.0 m, B 11.0 m, C 12.0 m, and D 26.0 m. Determine the magnitude and directional angle for the resultant that occurs when these vectors are added together. A

On a safari, a team of naturalists sets out toward a research station located 4.8 km away in a direction 42 north of east. After traveling in a straight line for 2.4 km, they stop and discover that they have been traveling 22 north of east, because their guide misread his compass. What are (a) the magnitude and (b) the direction (relative to due east) of the displacement vector now required to bring the team to the research station? *

Two geological field teams are working in a remote area. A global positioning system (GPS) tracker at their base camp shows the location of the first team as 38 km away, north of west, and the second team as 29 km away, east of north. When the first team uses its GPS to check the position of the second team, what does the GPS give for the second teams (a) distance from them and (b) direction, measured from due east?

A sailboat race course consists of four legs, defined by the displacement vectors , , , and , as the drawing indicates. The magnitudes of the first three vectors are A 3.20 km, B 5.10 km, and C 4.80 km. The finish line of the course coincides with the starting line. Using the data in the drawing, find the distance of the fourth leg and the angle . *

Multiple-Concept Example 9 deals with the concepts that are important in this problem. A grasshopper makes four jumps. The displacement vectors are (1) 27.0 cm, due west; (2) 23.0 cm, 35.0 south of west; (3) 28.0 cm, 55.0 south of east; and (4) 35.0 cm, 63.0 north of east. Find the magnitude and direction of the resultant displacement. Express the direction with respect to due west. D

Vector has a magnitude of 145 units and points 35.0 north of west. Vector points 65.0 east of north. Vector points 15.0 west of south. These three vectors add to give a resultant vector that is zero. Using components, find the magnitudes of (a) vector and (b) vector . *

The route followed by a hiker consists of three displacement vectors , , and . Vector is along a measured trail and is 1550 m in a direc A tion25.0 north of east. Vector is not along a measured trail, but the hiker uses a compass and knows that the direction is 41.0 east of south. Similarly, the direction of vector is 35.0 north of west. The hiker ends up back where she started. Therefore, it follows that the resultant displacement is zero, or . Find the magnitudes of (a) vector and (b) vector . C

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? 58. A monkey is chained to a stake in the ground. The stake is 3.00 m from a vertical pole, and the chain is 3.40 m long. How high can the monkey climb up the pole?

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 ostrichs velocity component that is directed (a) due north and (b) due west?

The volume of liquid flowing per second is called the volume flow rate Q and has the dimensions of [L]3 /[T]. The flow rate of a liquid through a hypodermic needle during an injection can be estimated with the following equation: The length and radius of the needle are L and R, respectively, both of which have the dimension [L]. The pressures at opposite ends of the needle are P2 and P1, both of which have the dimensions of [M]/{[L][T]2 }. The symbol represents the viscosity of the liquid and has the dimensions of [M]/{[L][T]}. The symbol stands for pi and, like the number 8 and the exponent n, has no dimensions. Using dimensional analysis, determine the value of n in the expression for Q. 6

An ocean liner leaves New York City and travels 18.0 north of east for 155 km. How far east and how far north has it gone? In other words, what are the magnitudes of the components of the ships displacement vector in the directions (a) due east and (b) due north?

A pilot flies her route in two straight-line segments. The displacement vector for the first segment has a magnitude of 244 km and a direction 30.0 north of east. The displacement vector for the second segment has a magnitude of 175 km and a direction due west. The resultant displacement vector is and makes an angle  with the direction due east. Using the component method, find the magnitude of and the directional angle .

A circus performer begins his act by walking out along a nearly horizontal high wire. He slips and falls to the safety net, 25.0 ft below. The magnitude of his displacement from the beginning of the walk to the net is 26.7 ft. (a) How far out along the high wire did he walk? (b) Find the angle that his displacement vector makes below the horizontal.

A force vector points at an angle of 52 above the x axis. It has a y component of 290 newtons. Find (a) the magnitude and (b) the x component of the force vector. *

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 . A

Three forces act on an object, as indicated in the drawing. Force has a magnitude of 21.0 newtons (21.0 N) and is directed 30.0 to the left of the y axis. Force has a magnitude of 15.0 N and points along the axis. What must be the magnitude and direction (specified by the angle  in the drawing) of the third force such that the vector sum of the three forces is 0 N?

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).

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 the height of his building is more than 1.50 times the height of 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, whereas 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. F

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 x direction, and due north is the y direction. C B  177 units, 23.0 north of east B B  222 units, 35.0 south of east A B  113 units, 60.0 south of west * 55