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Free falling …

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ACCELERATION DUE TO GRAVITY All bodies in free fall (that is no air resistance) near the Earth's surface have the same downward acceleration of: g = 9.8 m/s 2 NOTE: A body in free fall has the same downward acceleration whether it starts from rest or has an initial velocity in some direction.

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Okay let’s drop a ball from the top of a cliff… What happens to the velocity each second? gtgt V f = 0 + (10 m/s 2 )(1s) = 10 m/s V f = 10m/s + (10 m/s 2 )(1s) = 20 m/s or V f = 0 + (10 m/s 2 )(2s) = 20 m/s

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What happens to the distance traveled each second? d = 0 + ½ (10 m/s 2 )(1s) 2 = 5 m d = 0 + ½ (10 m/s 2 )(2s) 2 = 20 m d

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Example 1: A ball is dropped from rest at a height of 50.0 m above the ground. a. What is its speed just before it hits the ground? v o = 0 m/s d = 50 m g = 10 m/s 2 v f = ? b. How long does it take to reach the ground? (0 m/s) 2 + 2(9.8 m/s 2 )(50.0m) V f = 31.3 m/s = (31.6 m/s – 0) 9.8 m/s 2 = 3.22 sec d

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Let’s look at a coin toss. The coin leaves your hand at 6 m/s and travels upward. The coin speed begins to decrease the moment it leaves your hand. The rate of deceleration is -9.80 m/s 2 The velocity is zero at the top of its trajectory.

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V o = 0 Then the coin starts the down trip And begins to accelerate downward at the rate of + 9.80 m/s 2 When it gets back to your hand its velocity is? The same velocity that it left your hand with 6 m/s Why?

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Let’s look at another example of an up down problem. V = 0 m/s - 9.80 m/s 2 + 9.80 m/s 2 up down

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Example 2 A stone is thrown straight upward with a speed of 20.0 m/s. a. How long did the trip take? v o = 20 m/s v f = 0 m/s g = -9.8 m/s 2 b. How high will the stone go? = 0 – 20 m/s - 9.8 m/s 2 = 2.04 s d d = -(20 m/s) 2 2(-9.8 m/s 2 ) = 20.4 m d d= 0 + ½ (9.8m/s 2 )(2.04s) 2 d= 20.4 m Or using the down trip… d = V f 2 – V o 2 2a t total = 2(t up ) = 4.08 s

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Chapter 2 Correct Answers 4. 50,000 years 7. 52 meters 9. 7.2 km 12. 8.18 m/sec 2 18. (a) 8 m/sec (b) motorcyclist A has greatest v since a is smaller 19.(a) 11.41 sec (b)44.7m/sec 2 25. (a) 81.67 m/sec 2 (b)0.17 s 28. 96.94 m/sec 35. 13.5 sec 41. 1.11 sec 54. 8.18 m/sec 56. 2.5 meters 58. (a) 2 m/sec 2 (b) 0 m/sec 2 (c) 3.33 m/sec 2 59. (a) -20 km/hr (b) 10 km/hr (c) 40 km/hr 60. (a) A--- positive B---zero C- --negative D--- positive (b) v A = 5 km/hr v B = 0 km/hr v C = -3.75 km/hr v d = 2.5 km/hr

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64. 5.6 m/sec 2 ; east 65. 91.48 m/s 66. 1.8 meters 67.(a) 4 sec (b) 4 sec 68. 0.47 seconds 69. 9.15 fields 70. a 2 = 4.5 m/sec 2 71. 43.73 m/sec downward 73. (a) 26,760 m (b) 6.76 m/sec 74. d 2 = 805 meters 75. d x = 19.56 meters 76. 5.63 s 77. 15.33 s 78. 6 m 79. v car = 13.14 m/s; at = 0.93 m/sec 2 80. 1.4 m/sec 2

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