The problems for this week are OPTIONAL.
We will finish our discussion of Giancoli Chapter 5 (circular motion and gravitation) and will likely start on Chapter 6 (work and energy) at the end of the week. The problems are for review of kinematics (in 1+1 and in 2+1) and of dynamics.
(1) If one car accelerates at a greater rate than another, does the first car neccessarily have a greater speed? Explain, using examples.
(2) Huck Finn skips at a speed of 0.6 m/s across his raft (he walks perpendicular to the raft's motion relative to the shore). The raft is drifting down the Mississippi River at a speed of 1.70 m/s relative to the river bank. What is Huck's velocity (speed and direction) relative to the river bank?
(3) An airplane is heading due south at a speed of 600 km/hr. If a wind begins blowing from the southwest at a speed of 100 km/hr (average), calculate: (a) the velocity (magnitude and direction) of the plane relative to the ground, and (b) how far from its intended position will it be after 10 min if the pilot takes no corrective action. (c) In what direction should the pilot aim the plane in so that it will fly due south?
(4) For an object falling freely from rest, show that the distance traveled during each succeeding second increases in the ratios of successive odd integers (1, 3, 5, 7, 9, etc.). This was first shown by Galileo.
NOTE The first second is from t = 0 to t = 1s. The next second is from t=1s to t=2s, etc.. So Galileo says that the distance travelled between t=1s and t=2s should be 3 times the distance travelled between t=0s and t=1s and so on for all the rest of the sequence.
(5) A skier is accelerating down a 30.0° hill at 1.8 m/s^2. What is the vertical component of her acceleration? (b) How long will it take her to reach the bottom of the hill, assuming she starts from rest and accelerates uniformly, if the elevation change is 335 m?
(6) Ch 4 Question 2
(7) A set of keys hangs by a string from a car's rearview mirror. While the car accelerates at a constant rate in the horizontal direction from a stoplight to 28 m/s in 6.0 s, what angle does the string make with the vertical?
(8) On an icy day, you worry about parking your car in your driveway, which has an incline of 12°. Your neighbor's driveway has an incline of 9.0°, and the driveway across the street is at 6.0°. The coefficient of static friction between tire rubber and ice is 0.13. Which driveway(s) will be safe to park in?
(9) What would your bathroom scale read if you weighed yourself on an inclined plane? Assume the mechanism functions properly, even at an angle.
(10) The cliff divers push off horizontally from platforms about 35m above the water, but they must clear rocky outcrops at water leel that extend out into the water 5.0m from the base of the cliff directly under their feet. What minimum pushoff speed is necessary to clear the rocks? How long are they in the air?