**Unit 3: Motion in
Two-Dimensions**

**Problem Set A**

The following selection of problems are sample problems. Individual student problem sets will vary since numerical information is randomly-generated.

**Directions:**

For the following problems:

- Compute the unknown quantity and enter the answer in the blank.
- Use 9.8 m/s/s as the numerical value of g for situations upon Earth.
- Do not round any computed numbers until the last calculation.
- Unless told otherwise, enter your answers accurate to the second decimal place.
- Unless told otherwise, enter positive numbers for your answers.

**Multiple Choice:**

Which of the following statements are true? Choose all that apply by listing their letter in alphabetical order with no spaces, commas, or other marks between letters.

a. It is possible for a person to take a trip and to have a resultant displacement which is greater than the distance traveled during the trip.

b. The resultant of A + B + C (in the diagram at the right) would have a direction of 315 degrees.

c. The order in which four vectors are added would effect the magnitude and the direction of a resultant.

d. Adding two vectors of magnitude 12 units and 16 units can yield resultants with any magnitude between 0 units and 28 units.

e. A person walks 50 feet west, 40 feet south, 20 feet east and 40 feet north. The displacement would be 30 feet, west and the distance would be 70 feet.

f. Adding two vectors of magnitude 6 units and 8 units can only yield resultant values of 2 units, 10 units, and 14 units.

g. A person walks 200 feet north and 300 feet south. The displacement would be 500 feet and the distance would be 100 feet, south.

h. Vector D in the diagram at the right has a direction of 260 degrees.

i. Vector A + vector B produce the resultant C. Vector A - vector B produce the resultant D. One can be sure that vectors C and D would have the same magnitude but directions which are exactly opposite each other (i.e., 180 degrees different).

j. Vector C in the diagram at the right has a direction of 60 degrees.

(List all in alphabetical order with no spaces or punctuation marks.)

**Problem 1:**

A man lost in a maze makes three consecutive displacements such that at the end of the walk he is right back where he started. The first displacement is 8.4 m westward, and the second is 7.9 m northward. Find the magnitude (in meters) of the third displacement.

**Problem 2:**

(Referring to the previous problem.) Find the direction (in degrees) of the third displacement. (Use the counter-clockwise from east convention.)

**Problem 3:**

A quarterback takes the ball from the line of scrimmage, runs backward for 6.7 yards, then sideways parallel to the line of scrimmage for 8 yards. At this point, he throws a 27.2-yard forward pass straight down field perpendicular to the line of scrimmage. What is the magnitude (in yards) of the football's resultant displacement?

**Problem 4:**

A shopper pushing a cart through a store moves a distance 21.7 m down one aisle then makes a 90 degree turn to his right and moves 8.9 m. He then makes another 90 degree turn to his left and moves 12.2 m. How far (in meters) is the shopper away from his original position?

**Problem 5:**

(Referring to the previous problem.) What is the direction (in degrees) of the shopper's displacement (relative to the original line of motion)? (Enter a positive value.)

**Problem 6:**

What is the magnitude of the resultant displacement (in meters) of a walk of 46.1 m followed by a walk of 64.8 m when both displacements are in the eastward direction?

**Problem 7:**

(Referring to the previous problem.) What is the magnitude of the resultant displacement (in meters) in a situation in which the 64.8 m walk is in the direction opposite the 46.1 m walk?

**Problem 8:**

A waitress walks a distance of 53.3 feet west amd then 25.8 feet south. What is the resulting displacement (in feet) from its starting point at the end of this movement?

**Problem 9:**

Referring to the previous problem. Determine the direction of the waitress's displacement. Express your answer in degrees as a the counter-clockwise angle of rotation from due east.

**Problem 10:**

A jogger runs 70 m due west, then changes direction and runs 76 m due north. She then heads west again and finishes a total distance of 371 m from her starting location. What was the length (in meters) of her third displacement?

**Problem 11:**

(Referring to the previous problem.) What was the direction (in degrees) of the resulting displacement for the three legs of this jog? (Use the counter-clockwise from east convention.)

**Problem 12:**

A roller coaster travels 81 ft at an angle of 17.1 degree above the horizontal. How far (in feet) does it move horizontally?

**Problem 13:**

(Referring to the previous problem.) How far (in feet) does it move vertically?

**Problem 14:**

A submarine dives at an angle of 16.1 degrees with the horizontal and follows a straight-line path for a total distance of 124.1 m. How far (in meters) is the submarine below the surface of the water?

**Problem 15:**

During the Vector Addition lab, Mac and Tosh start at the classroom door and walk 7.6 m, north, 13.4 m west, 13.5 m south, 8.8 m west, and 4.2 m, north. Determine the magnitude of the resulting displacement (in meters) of Mac and Tosh.

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