Problem Solving

1. Problem Solving Created for BW Physics by Dick Heckathorn 11 August 2K + 6

2. Objectives We will learn how to: • use the GUESS method to solve problems. • use units when solving problems. • convert from one unit to another.

3. Step One Conceptualize - think about and understand the situation - make a drawing/sketch - focus on information provided - focus on expected result - use own experience

4. Step Two Categorize - simplify the problem by remove details which are not important - see of there are statements that indicates that it is a plug-in problem - or that it is an analysis problem

5. The Problem to be Solved This morning your instructor traveled 26.4 miles from his home to work in 0.6 hours. Find his average speed in miles per hour. Do you have a good idea of what is going on?

6. You will now be introduced to a method of solving this problem using the G U E S S method.

7. The Letters Stand For: G - Given U - Unknown E - Equation S - Substitute S - Solve

8. As you proceed through this five step process, you will need to write all the necessary information on a piece of paper as you complete each step.

9. When the last step is completed, you will have the solution along with your work showing how you arrived at the answer.

10. Remember, your instructor feels that the steps you use to solve the problem are more important than the answer. Therefore he insists that you show each step!!!

11. Sounds easy so let’s begin.

12. The Problem Stated Again This morning your instructor traveled 26.4 miles from his home to work in 0.6 hours. Find his average speed in miles per hour.

13. Your First Step Find a given quantity?

14. Identifying a Given Quantity One Given quantity is 26.4 miles which represents a distance. One represents distance with a ‘d’. Note… this is a small ‘d ’.

15. Properly Writing a Given Quantity d = 26.4 miles Note… the unit ‘miles’ must be included.

16. The Problem Stated Again This morning your instructor traveled 26.4 miles from his home to work in 0.6 hours. Find his average speed in miles per hour.

17. Are there other Given quantities? The answer is yes so:

18. Identifying a second Given (G) A second Given quantity is 0.6 hours which represents a quantity of time. One always uses 't' for time. Note that this is a small't’.

19. Adding a Second Variable Thus one adds to: d = 26.4 miles t = 0.6 hours a second variable

20. Are there any other Given quantities?

21. The Problem Stated Again This morning your instructor traveled 26.4 miles from his home to work in 0.6 hours. Find his average speed in miles per hour.

22. The answer is no. So on to the next step.

23. Identifying theUnknown (U) The unknown is ‘speed’ which is represented by the letter ‘v’. Note… this is a small ‘v’.

24. Adding the Unknown Variable d = 26.4 miles t = 0.6 hour v = ______

25. A Problems That Must Be Addressed Note…Many if not all of you will think the word ‘rate’ represents how fast something is moving. While this is the word used in math classes for this purpose, it is not used for this purpose in physics.

26. A Challenge Your instructor will expect you to work hard to omit the word ‘rate’ when describing how fast something is moving and instead, use the word ‘speed’.

27. Speed vs Velocity There is another word, ‘velocity’, which also describes how fast something is moving. It’s definition differs from ‘speed’. Stay tuned for the definition of ‘velocity’.

28. Identifying the Equation (E) The 3rd step in solving a problem is to identify the Equation that relates the Given quantities (d) and (t) to the Unknown quantity (v).

29. One might have learned that: and in symbol form:

30. Adding the (E)quation d = 26.4 miles t = 0.6 hours v = ______

31. Substituting (S) variables into the Equation The 4th step is to substitute the variables (d) and (t) into the equation:

32. Your Work so Far d = 26.4 miles t = 0.6 hours v = ______

33. Solving (S) to find the answer. The 5th step is to Solve the problem. To do this one performs the necessary calculation usually using a calculator.

34. Your Work for this Problem d = 26.4 miles t = 0.6 hours v = ______

35. Note that your instructor wrote the units in fraction form with a distinct numerator and denominator. You are encouraged to do the same as doing so will aid you when solving problems.

36. Your Final Written Product G d = 26.4 miles t = 0.6 hours v = ______ U E S S

37. A Question “Does the answer seem reasonable?”

38. Another Question Do the units of the answer appear to be correct based on the information given?

39. Remember that the units talk. But they can ‘talk’ only if you faithfully keep track of them. Failure to do so will cause your instructor extreme disappointment. In fact it will cause point loss beginning with the first step omitted.

40. In solving this problem, the units help to tell us if we are correct or not. Since the units are identical to that which were identified in the unknown statement, one can safely conclude that the problem was set up and solved correctly.

41. There is a possibility that one made a careless mistake, but this is generally not the case. Your instructor will remind you and remind you and remind you… “Let the Units Do the Talking.”

42. Units Are Important!!! Since they talk, be sure to listen for they say much. But remember, they will not talk unless they are available. So faithfully keep track of them.

43. The Problem Changed Slightly This morning your instructor traveled 26.4 miles from his home to CVCA in 36 minutes. Find his average speed in miles per hour.

44. Will expressing the time in minutes change how one does the problem? The answer is yes, so lets see the difference.

45. The variable ‘d’ -> 26.4 miles is the same.

46. Your Work so Far d = 26.4 miles

47. The known variable ‘t’ is expressed as 36 minutes.

48. Your Work so Far d = 26.4 miles t = 36 min

49. Identifying theUnknown (U) The unknown is ‘speed’ which is represented by the letter ‘v’.

50. Your Work so Far d = 26.4 miles t = 36 min v = ______