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27 Freely Falling Objects (neglect air resistance) 39. (I) A stone is dropped from the top of a cliff. It is seen to hit the ground below after 3.55 5. How high is the cliff? 41. (II) A ball player catches a hall 3.4 s after throwing it vertically upward. With what speed did he throw it, and what height did it reach? 43. (II) A kangaroo jumps straight up to a vertical height of 1.45 m. How long was it in the air before returning to Earth? 47. (II) For an object falling freely from rest, show that the distance traveled during each successive second increases in the ratio of successive odd integers (1, 3, 5, etc.). (This was first shown by Galileo.) See Figs. 219 and 222. 49. (II) A helicopter is ascending vertically with a speed of 5.40 m/s. At a height of 105 m above the Earth, a package is dropped from the helicopter. How much time does it take for the package to reach the ground? [Hint: What is v0 for the package?] 28 Graphical Analysis 55. (II) Figure 242 shows the velocity of a train as a function of time. (a) At what time was its velocity greatest? (b) During what periods, if any, was the velocity constant? (c) During what periods, if any, was the acceleration constant? (d) When was the magnitude of the acceleration greatest? 57. (II) The position of a rabbit along a straight tunnel as a function of time is plotted in Fig. 244. What is its instantaneous velocity (0) at t = 10.0 s and (b) at t = 30.0 5? What is its average velocity (c) between t= 0 and t = 5.0 s, (d) between t= 25.0 s and t = 30.0 s, and (e) between t = 40.0 s and t= 50.0 s