3. one point, from Lectures 2-4, involves calculation, not necessary to type.

(b) .6 from Lectures 3 and 4, Falling Down the Stairwell of Sterling Hall. This problem will not have a ``nice '' whole-number answer. First estimate how tall Sterling Hall is in meters from the floor of the basement to the roof. You don't have to see the building to do this. I will tell you that there is a basement and then four stories, and the ceilings are higher than in an average house. Call the estimated height of the building h. You must explain your reasoning to get credit for your estimate. (.3)
Next calculate how long a time t it takes for an object dropped down the stairwell from the ceiling of the top floor to hit the floor of the basement. Use h=½gt², g=10m/s², and whatever you estimated for h. (.3)

question 4, due Wednesday, September 17

4. one point, from Lectures 4 and 5, involves time-consuming graphs, not necessary to type.

Ten Tedious but Necessary Spacetime Diagrams. Draw spacetime diagrams (graphs) for the five kinds of motion given below, on axes with the axis x for position in meters and the axis t for time in seconds.

• Plot each one first with the x axis vertical and the t axis horizontal,
• then with the x axis horizontal and the t axis vertical, to get ten graphs, worth .1 point apiece.

1 to 2 inches is a good size to allow for each graph. If you want to get partial credit in case of a careless math error, show your calculations in a table .

• Label the axes with the seconds and meters.
• Use a ruler, and draw the lines carefully and accurately.
• Ask for help if this gives you trouble.

Here are the conditions of motion. Don't forget to do 2 graphs for each. Draw all these graphs accurately!

• (1) Standing still at x=3m from time t=0 to time t=5s.
• (2) Starting at x=0 and moving forward with constant velocity v=9m/s from time t=0 to time t=5s.
• (3) Use the same scale as in the second graph. Starting at x=0 and moving forward with constant velocity v=3m/s from time t=0 to time t=5s. Notice the different looks of (2) and (3) (fast and slow).
• (4) Starting at rest (v=0) at x=0 and accelerating uniformly with x=3t² (acceleration equals 6 meters per second squared) from time t=0 to time t=5s.
• (5) Starting with speed v=30m/s at x=0 and decelerating uniformly with x= -3t² (acceleration equals minus 6 meters per second squared) from time t=0 to time t=5s. This one is the hardest. To be safe, tabulate the motion one second at a time. Notice the different looks of (4) and (5) (speeding up and slowing down).

Revised September 4, 1997.