Lab 07
Name:
Start time: border="0" Number of questions: 13
This set of questions goes with the pages of applets and activities for Lab 07.  Use the applets and activities there to answer the questions.
 

Question 1  (1 point)
Refer to lab page 2. Two workmen want to carry a ladder around a corner where one corridor meets another. Whether or not the ladder fits depends on the length of the ladder and the widths of the two corridors. The interactive figure lets you experiment with different combinations of these distances. It gives a view looking down on the intersection, with the ladder represented by a red line segment.
You can drag points C and D to change the widths of the corridors. The picture is scaled so that the numbers reported are the widths of the corridors in feet. Drag point A to change the length of the ladder. After the distances are set, move point B to see if the ladder fits around the corner. When the ladder gouges the wall, it disappears. The goal is to make the ladder as long as possible and have it go around the corner without disappearing.

Press the refresh button to restore the initial picture. With these corridor widths, what is the longest that the ladder can be to fit around the corner?


 


Question 2  (.5 points)
Refer to lab page 2. Drag D to reset the side corridor width to be 4, and leave the top corridor width 6. Now what is the longest that the ladder can be?


 


Question 3  (.5 points)
Refer to lab page 2. How about making the side corridor 2 and the top corridor 3?


 


Question 4  (.5 points)
How can you use geometry to account for the relationship between the answer to question 2 and question 3?

 


Question 5  (.5 points)
Refer to lab page 2. Click the button marked Show Angle and guide line to give some auxiliary information about how the ladder moves. The guide line is the thin blue line that tracks the ladder. It makes an angle with its vertex at point B. How do the ladder length and the guide line length compare when the ladder has disappeared?

 


Question 6  (.5 points)
Refer to lab page 2. What happens to the reported angle as point B moves further and further to the left?

 


Question 7  (.5 points)
Refer to lab page 2. What is the furthest to the right that B can move, and what happens to the reported angle there?

 


Question 8  (1 point)
Refer to lab page 2. Set the corridor widths to both be 6 feet. What angle makes the guide line length the shortest? (Answer in degrees.)


 


Question 9  (1 point)
Refer to lab page 2. What is the relation between the ladder length and the guide line length?

 


Question 10  (.5 points)
Consider the picture as augmented below. The guide line has two parts, labeled L1 and L2, for the part of the guide line in each corridor. The angle is labeled x. Identify a right triangle and use it to write an equation giving L1 as a function of x. (Note that L1 is not in general the same as the length of the ladder.)

 


Question 11  (.5 points)
Write an equation giving L2 as a function of x.


Question 12  (1 point)
The guide line length L is L1 + L2. Use the Grapher on lab page 3 to plot L as a function of x. Examine the graph to find the minimum value of L, and compare the answer to the experimental value for the longest ladder obtained in problem 1.



Question 13  (2 points)