1. A car travels from to in a time of 2.7 h. ( 27,0, 15 mi  130,0, 107 mi  mi = miles; h

1. A car travels from to in a time of 2.7 h. ( 27,0, 15 mi  130,0, 107 mi  mi = miles; h = hours) Keep all units in this problem in terms of miles and hours. (a) What was the change in position of the car? (b) Find the unit vector in the direction of the car’s change in position. (c) Write the car’s change in position in the form change-in-position = magnitude times unit-vector (as was done in class for average velocity). (d) Find the car’s average velocity. Write the answer in the form average-velocity = (magnitude of average velocity vector) times (unit-vector in direction of average velocity vector). (e) What are the angles that the average velocity vector makes with the x-, y-, and z- axes? (See if you can figure this out. See the discussion and examples on pages18-19.) That is, find the angles x, y, and z. 2. (This problem has nothing to do with the physics we discussed in class—it is just a problem in reasoning.) The photograph below shows the underside of a large mushroom (about 5 inches in diameter). The radial partitions are called gills. (a) Find the approximate average angular width in radians of the air gap between two adjacent gills. Be sure to carefully explain how you obtained your answer. (b) How would your answer change if the photograph were enlarged to twice the size shown below? Explain.

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