Physics 163

Unit 3: Motion in Two-Dimensions

Problem Set A

 

Overview:

Problem Set A targets your ability to use right angle trigonometry and vector addition principles to analyze physical situations involving displacement vectors and to interpret and solve such word story problems. There are about five skills or conceptual understandings which you will need to have a solid grasp of in order to be successful on Problem Set A:

  1. Displacement vectors can be added using a head-to-tail method of vector addition. If adding vector B to vector A, then vector A should first be drawn; then vector B should be added to it by drawing it so that the tail of vector B starts at the location that the head of vector A ends. The resultant vector is then drawn from the tail of A (starting point) to the head of B (finishing point). The resultant is equivalent to the sum of the individual vectors. In Problem Set A, you will have to be able to read the word story problem and sketch an appropriate vector addition diagram. The head-to-tail addition of vectors can be reviewed at The Physics Classroom.
  2. One convention commonly used for expressing the direction of vectors is the counter-clockwise from east convention. The direction of a vector is represented as the counter-clockwise angle of rotation which the vector makes with due East. The use of this convention can be reviewed at The Physics Classroom.
  3. Vectors which are added at right angles to each other will sum to a resultant vector which is the hypotenuse of a right triangle. The Pythagorean theorem can be used to relate the magnitude of the hypotenuse to the magnitudes of the other two sides of the triangle. The angles within the right triangle can be determined from knowledge of the length of the sides using SOH CAH TOA. These basic principles of right triangle trigonometry can be reviewed at The Physics Classroom.
  4. A vector which makes an angle with to one of the axes can be projected onto the axes to determine its components. SOH CAH TOA can be used to resolve such a vector and determine the magnitudes of its x- and y- components. The method of vector resolution can be reviewed at The Physics Classroom.
  5. The order in which vectors are added does not effect the magnitude or direction of the resultant. This principle can be reviewed at the Multimedia Physics Studios.

View Sample Problem Set.

 

Problem

Description

Audio Link
MC

A conceptual question; the database creates at random 10 true-false statements which must be evaluated properly

1

Addition of three vectors; use of Pythagorean theorem to determine the magnitude of the third vector

2

Extension of Problem 1; addition of three vectors; use of SOH CAH TOA to determine a direction

3

Addition of three vectors; use of Pythagorean theorem to determine resultant

4

Addition of three vectors; use of Pythagorean theorem to determine the magnitude of the resultant

5

Extension of Problem 4; addition of three vectors; use of SOH CAH TOA to determine a direction

6

Addition of two vectors along the same line of motion

7

Addition of two vectors having opposite directions

8

Addition of two vectors; use of Pythagorean theorem to determine the magnitude of the resultant

9

Extension of Problem 8; addition of two vectors; use of SOH CAH TOA to determine a direction

10

Addition of three vectors; use of Pythagorean theorem to determine the magnitude of the third vector; requires thoughtful analysis

11

Extension of Problem 10; addition of three vectors; use of SOH CAH TOA to determine a direction

12

A straight-forward vector resolution problem

13

Extension of Problem 12; a straight-forward vector resolution problem

14

A straight-forward vector resolution problem

15

Addition of five vectors; use of Pythagorean theorem to determine the magnitude of the resultant; must construct and simplify a vector diagram

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