**Free Fall Acceleration**

40E. Raindrops fall 700 m from a cloud to the ground. (a) If they were not slowed by air resistance, how fast would the drops be moving when they struck the ground? (b) Would it be safe to walk outside during a rainstorm?

41E. At a construction site a pipe wrench struck the ground with a speed of 24 m/s. (a) From what height was it inadvertently dropped? (b) How long was it falling? (c) Sketch graphs of y and a versus t for the wrench.

42E. A hoodlum throws a stone vertically downward with an initial speed of 12.0 mls from the roof of a building, 30.0 m above the ground. (a) How long does it take the stone to reach the ground? (b) What is the speed of the tone at impact?

43E. (a) With what speed must a ball be thrown vertically from ground level to rise to a maximum height of 50 m? (b) How long will it be in the air? (c) Sketch graphs of y, v, and a versus t for the ball. On the first two graphs indicate the time a~ which 50 m is reached.

44E. The Zero Gravity Research Facility at the NASA Lewis Research Center ,includes a 145 m drop tower. This is an evacuated vertical tower through which. among other possibilities, aim diameter sphere containing an experimental package can be dropped. (a) How long is the sphere in free fall? (b) What is its speed just as it reaches a catching device of the tower? (c) When caught, the sphere experiences an average deceleration of 25g as its speed is reduced zero. Through what distance does it travel during the deceleration?

45E. A rock is dropped from a 100-m-high cliff. How long does it take to fall (a) the first 50 m and (b) the second 50 m?

46P. A ball is thrown down vertically with an initial speed from a height of h. (a) What is its speed just before it strikes tile ground? (b) How long the ball take to reach tile ground? What be the answers to (c) part a and (d) part of the ball were thrown upward from the same height and with the same initial speed? Before solving any equations, decide whether the answers to (c) and (d) should be greater than. less than, or the same as in (a) and (b).

47P. A startled armadillo leaps upward, rising 0.544 m in the first 0.200, s. (a) What is its initial speed as it leaves the ground? (b) What is its speed at the height of 0.544 m? (c) How much higher does it go?

48P. A rock is dropped (from rest) from the top of a 60-m-tall building. How far above the ground is the rock before it reaches the ground?

49P. A key falls from a bridge that is 45 m above the water. It falls directly into a model boat. moving with constant velocity, that is 12 m from the point of impact when the key is released. What is the speed of the boat?

5OP. A ball is thrown vertically downward from the top of a 36.6-m-tall building. The ball passes the top of a window that is 12.2 m above the round 2.00 s after being thrown.What is the speed of the ball as it passes the top of the window?

51P. A ball of moist clay falls 15.0 m to the ground. It is in contact with the ground for 20.0 ms before stopping. What is the average acceleration of the ball during the time it is in contact with the ground? (Treat the ball as a article.)

52P. A model rocket fired vertically from the ground ascends with a constant vertical acceleration of 4.00 m/s2 for 6.00 s. Its fuel is then exhausted, so it continues upward as a free-fall particle and then falls back down. (a) What is the maximum altitude reached? (b) What is the total time elapsed from takeoff until the rocket strikes the ground?

53P. To test the quality of a tennis ball. you drop it onto the floor from a height of 4.00 m. It rebounds to a height of 2.00 m. If the ball is in contact with the floor for 12.0 ms. what is its average acceleration during that contact?

54P. A basketball player. standing near the basket to grab a rebound. jumps 76.0 cm vertically. How much (total) time does the player spend (a) in the top 15.0 of this jump and (b) in the bottom 15.0 ? Does this help explain why such players seem to hang in the air at the tops of their jumps?

55P. Water drips from the nozzle of a shower onto the floor 200 cm below. The drops fall at regular (equal) intervals of time. the first drop striking the floor at the instant the fourth drop begins to fall. Find the locations of the second and third. drops when the first strikes the floor.

56P. A ball is shot vertically upward from the surface of a planet in a distant solar system. A plot of y versus t for the ball is shown in.Where y is the height of the ball above its starting point and the instant the ball is shot. What are the magnitudes of (a) the free-fall acceleration on the planet and (b) the initial velocity of the ball?

57P. Two diamonds begin a free fall from rest from the same height, 1.0 s apart. How long after the first diamond begins to fall will the two diamonds be 10 m apart?

58P. A certain juggler usually tosses balls vertically to a height. To what height must they be tossed if they are to spend twice as much time in the air?

59P. A hot-air balloon is ascending at the rate of 12 is 80 m above the ground when a package is dropped over the side. (a) How long does the package take to reach the ground? (b) With what speed does it hit the ground?

60P. A stone is dropped into a river from a bridge 43.9 m above the water. Another stone is thrown vertically down 1.00 s after the first is dropped. Both stones strike the water at the same time. (a) What is the initial speed of the second stone? (b) Plot velocity versus time on a graph for each stone. taking zero time as the instant the first stone is released.

61P. An elevator without a ceiling is ascending with a constant speed of 10 m/s. A boy on the elevator shoots a ball directly upward. from a height of 2.0 m above the elevator floor. just as the elevator floor is 28 m above the ground. The initial speed of the ball with respect to the elevator is 20 m/s. (a) What maximum height above the ground does the ball reach? (b) How long does the ball take to return to the elevator floor?

62P. A stone is thrown vertically upward. On its way up it passes point A with speed v, and point B. 3.00 m higher than A, with speed Calculate (a) the speed . and (b) the maximum height reached by the stone above point B.

63P.Shows a simple device for measuring your reaction time. It consists of a cardboard strip marked with a scale and two large dots. A friend holds the strip vertically, with thumb and forefinger at the dot on the right in . You then position your thumb and forefinger at the other dot (on the left in being careful not to touch the strip. Your friend releases the strip. and you try to pinch it as soon as possible after you see it begin to fall. The mark at the place where you pinch the strip gives your reaction time. (a) How far from the lower dot should you place the 50.0 ms mark? (b) How much higher should the marks for 100, 150, 200, and 250 ms be? (For example, should the 100 ms marker be two times as far from the dot as the 50 ms

marker? Can you find any pattern in the answers?)

64P. A parachutist bails out and freely falls 50 m. Then the parachute opens, and thereafter she decelerates at 2.0 . She reaches the ground with.a speed of 3.0 m/s. (a). How long is the parachutist in the air? (b) At what height does the fall begin?

6SP. A drowsy cat spots a flowerpot that sails first up and then down past an open window. The pot is in view for a total of 0.50 s, and the top-to-bottom height of the window is 2.00 m. How high above the window top does the flowerpot go?