41. 42. 43. M. 47. 48. 49. (II) A ball player catches a ball 3.4s after throwing it vertically upward. With what speed did he throw it, and what height did it reach? (I1) A baseball is hit almost straight up into the air with a speed of 25 m/s. Estimate (a) how high it goes. (b) how long it is in the air. (c) What factors make this an estimate? (II) A kangaroo jumps straight up to a vertical height of 1.45m. How long was it in the air before returning to Earth? (I1) The best rebounders in basketball have a vertical leap (that is, the vertical movement of a fixed point on their body) of about 120 cm. (a) What is their initial \"launch\" speed off the ground? (b) How long are they in the air? 5. (II) An object starts from rest and falls under the influ- ence of gravity. Draw graphs of (a) its speed and (b) the distance it has fallen, as a function of time from t = 0 to t = 5.00s. Ignore air resistance. . (II) A stone is thrown vertically upward with a speed of 24.0m/s. (a) How fast is it moving when it is at a height of 13.0m? (b) How much time is required to reach this height? (c) Why are there two answers to (h)? (IT) 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. 2-19 and 2-22. (I1) A rocket rises vertically, from rest, with an accelera- tion of 3.2 m/s? until it runs out of fuel at an altitude of 775 m. After this point, its acceleration is that of gravity, downward. (a) What is the velocity of the rocket when it runs out of fuel? (b) How long does it take to reach this point? () What maximum altitude does the rocket reach? (d) How much time (total) does it take to reach maximum altitude? (e) With what velocity does it strike the Earth? (f) How long (total) is it in the air? (IT) A helicopter is ascending vertically with a speed of 5.40m/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 vy for the package?| S0. (II) Roger sees water balloons fall past his window. He notices that each balloon strikes the sidewalk 0.83 s after passing his window. Roger's room is on the third floor, 15m above the sidewalk. () How fast are the balloons trav- eling when they pass Roger's window? (b) Assuming the balloons are being released from rest, from what floor are they being released? Each floor of the dorm is 5.0 m high. - (II) Suppose you adjust your garden hose nozzle for a fast stream of water. You point the nozzle vertically upward at a height of 1.8m above the ground (Fig. 2-40). When you quickly turn off the nozzle, you hear the water striking the ground next to vou for another 2.5s. What is the water speed as it leaves the nozzle? 2 (m/s) 52. (1I1) A baseball is seen to pass upward by a window with a vertical speed of 14 m/s. If the ball was thrown by a person 18 m below on the street, (a) what was its initial speed, (b) what altitude does it reach, (c) when was it thrown, and (d) when does it reach the street again? . (IT) A falling stone takes 0.31s to travel past a window 2.2 m tall (Fig. 2-41). From what height above the top of the window did the n - stone fall? To travel this distance took 0.31s FIGURE 2-41 Problem 33. 54, (111) A rock is dropped from a sea cliff, and the sound of it striking the ocean is heard 3.4s later. If the speed of sound is 340 m/s, how high is the cliff? 2-8 Graphical Analysis 55. (II) Figure 2-42 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? () During what periods, if any, was the acceleration constant? (d) When was the magnitude of the acceleration greatest? 40 30 20 10 0 0 10 20 30 40 50 60 70 80 90 I(s) FIGURE 2-42 Problem 55. 56. (I1) A sports car accelerates approximately as shown in the velocitytime graph of Fig. 2-43. (The short flat spots in the curve represent manual shifting of the gears.) Estimate the car's average acceleration in (a) second gear and (b) fourth gear. 5th gear 4th gear 3rd gear p(m/s) 1st gear 0 f(s) 100 110 120