ADDITIONS TO HRW PROBLEMS AND PROBLEMS FROM OTHER TEXTS JUNE 3 - JUNE 6 HRW - CHAPTER 2 12. (g) Find the acceleration of the particle at t = 10 s. HRW - CHAPTER 3 24. (d) Also find the solution graphically. FISHBANE - CHAPTER 3 14. A particle moves in such a way that its coordinates are x(t) = (A)cos(wt) and y(t) = (A)sin(wt), where "w" stands for the Greek letter omega. Calculate the x- and y-components of the velocity and the acceleration of the particle. 28. A man in the crow's nest of a sailing ship moving through smooth seas at a steady 12 km/h accidentally lets a cannonball drop from his station, which is 8.5 m above the deck at the top of the mainmast. (a) Assuming that he dropped the ball from a position immediately adjacent to the vertical mast, where does the ball land with respect to the mast? (b) How long does it take for the ball to fall to the deck? (c) In the time it takes the ball to fall, what is the magnitude of the displacement of the ball as measured by the fixed observer? 60. An airplane is to fly due north from New Orleans to St. Louis, a distance of 673 mi. On that day and at the altitude of the flight, a wind blows from the west at a steady speed of 65 mi/h. The airplane can maintain an air speed of 180 mi/h. Ignore the periods of takeoff and landing. (a) In what direction must the airplane fly in order to arrive at St. Louis without changing direction? Draw a diagram and label this direction with an angle. Would this calculation change if the distance between the cities were twice as great? (b) What is the flying time for this flight? (c) Recalculate the flying time if the arplane heads due north until it reaches the latitude of St. Louis, and then flies due west, into the wind to reach the city. 65. A boat is required to traverse a river that is 150 m wide. The current in the river moves with a speed of 6 km/h. The boat can be rowed on still water with a speed of 10 km/h. Set up a convenient coordinate system in which to describe the various displacements. Using this coordinate system, write down the position vector of the boat at time t, assuming that the boat moves with uniform speed and that it leaves one side with the velocity vector making an angle theta with the direction of the river. Calculate theta such that the boat lands at a point exactly opposite the starting point. How long will the trip take? SERWAY - CHAPTER 3 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. FISHBANE - CHAPTER 4 24. (The figure for this problem is HRW Fig. 5-27, on page 92. Only the masses are different.) A force of magnitude 8.0 N pushes on a horizontally stacked set of blocks on a frictionless surface with masses m1 = 2.0 kg, m2 = 3.0 kg, and m3 = 4.0 kg. (a) What is the acceleration of the stack? (b) What are the forces on block 1, as well as the net force on this block. (c) Repeat part b for block 2. (d) Repeat part b for block 3. 26. Repeat problem 24, but this time with the blocks stacked in reverse order; that is, block 3 to the left and block 1 to the right.