PROBLEMS FROM SERWAY AND ADDITIONS TO FISHBANE PROBLEMS MAY 29 - JUNE 4 FISHBANE - CHAPTER 2 15. Also find the acceleration at t = 10 s. FISHBANE - CHAPTER 3 28. (c) The problem means to ask for the magnitude of the displacement of the ball as measured by the fixed observer. SERWAY - CHAPTER 2 6. A position-time graph for a particle moving along the y axis is shown in Figure (use Fishbane p. 56, FIGURE 3-3 (c)). (a) Find the average velocity in the time interval t = 1.5 s to t = 4 s. (b) Determine the instantaneous velocity at t = 2 s by estimating the slope of the tangent line at that point. (c) At what value of t is the velocity zero? 12. A 50 g superball traveling at 25 m/s bounces off a brick wall and rebounds at 22 m/s. A high-speed camera records this event. If the ball is in contact with the wall for 3.5 ms, what is the magnitude of the average acceleration of the ball during this time interval? (Note: 1 ms = 10^-3 s.) SERWAY - CHAPTER 3 3. A motorist drives south at 20 m/s for 3 min, then turns west and travels at 25 m/s for 2 min, and finally travels northwest at 30 m/s for 1 min. For this 6-min trip, find (a) the net vector displacement of the motorist, (b) the motorist's average speed, and (c) the average velocity of the motorist. 62. After delivering his toys in the usual manner, Santa decides to have some fun and slide down an icy roof. The roof is 8 m in length and makes an angle of 37 degrees with the horizontal. He starts from rest at the top of the roof and accelerates at the rate of 5 m/s^2. The edge of the roof is 6 m above a soft snowbank, on which Santa lands. Find (a) Santa's velocity components when he reaches the snowbank, (b) the total time he is in motion, and (c) the horizontal distance d between the house and the point where he lands in the snow. SERWAY - CHAPTER 4 45. A car of mass 1500 kg is being pulled up a loading ramp inclined at 30 degrees with the horizontal. The car is attached to a cable, which passes over a frictionless pulley to a 10000 N counterweight, which hangs vertically off the end of the ramp. (See FIG 5-33, p. 136 in FISHBANE. The car is M, and the counterweight is m.) Find (a) the tension in the cable, and (b) the acceleration of the system. (c) What mass should the counterweight have in order for the car to move down the incline at an acceleration of 2 m/s^2? (Ignore all friction.)