CHAPTER 6

  1. (P.173 Prob.18) A particle starts from rest at r0 = 9.0j m and moves in the xy-plane with the velocity shown in Figure P6.18. The particle passes through a wire hoop located at r1 = 20i m, then continues onward.
    a. At what time does the particle pass through the hoop?
    b. What is the value of v4y the y-component of the particle's velocity at t = 4 s?
    c. Calculate and plot the particle's trajectory from t = 0 s to t = 4 s.
  2. (P.173 Prob.24) A sailor climbs to the top of the mast, 15 m above the deck, to look for land while his ship moves steadily forward through calm waters at 4.0 m/s. Unfortunately, he drops his spyglass to the deck below.
    a. Where does it land with respect to the base of the mast below him?
    b. Where does it land with respect to a fisherman sitting at rest in his dinghy as the ship goes past? Assume that the fisherman is even with the mast at the instant the spyglass is dropped.
  3. (P.173 Prob.28) A ball is thrown toward a cliff of height h with a speed of 30 m/s and angle of 60° above horizontal. It land on the edge of the cliff 4.0 s later.
    a. How high is the cliff?
    b. What was the maximum height of the ball?
    c. What is the ball's impact speed?
  4. (P.174 Prob.36) An antiaircraft gun fires shells at 200 m/s at a 60° angle. An enemy place flies directly toward the gun at 300 m/s, 500  m off the ground. How far away (horizontally) must the plane be when the gun fires for the shell to hit the plane? Explain why you get two answers to this problem.
  5. (P.175 Prob.56) A sailboat is sailing due east at 8.0 mph. The wind appears to blow from the southwest at 12.0 mph.
    a. What are the true wind speed and direction?
    b. What are the true wind speed and direction if the wind appears to blow from the northeast at 12.0 mph?
  6. (P.176 Prob.66) Challenge Problem. A cat is chasing a mouse. The mouse runs in a straight line aat a speed of 1.5 m/s. If the cat leaps off the floor at a 30° angle and a speed of 4.0 m/s, at what distance behind the mouse should the cat leap in order to land on the poor mouse?