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Science Starter! Consider a ball thrown directly overhead. 1.Describe what happens to its velocity (in terms of speed and direction) on (a) the way up, and (b) the way down. 2.Describe what happens to its acceleration on (c) the way up, and (d) the way down.

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t (s)a (m/s 2 )v (m/s)y (m) 0 - 9.829.478.4 1- 9.819.6102.9 2- 9.89.8117.6 3- 9.80122.5 4- 9.8 117.6 5- 9.8-19.6102.9 6- 9.8-29.478.4 7- 9.8-39.244.1 8-9.8-490

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t (s)a (m/s 2 )v (m/s)y (m) 0 - 9.829.478.4 1- 9.819.6102.9 2- 9.89.8117.6 3- 9.80122.5 4- 9.8 117.6 5- 9.8-19.6102.9 6- 9.8-29.478.4 7- 9.8-39.244.1 8-9.8-490

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Key Ideas for Vertical Motion On way up: v is (+) a g = - 9.8 m/s 2 Speed decreases At highest point: v = 0 a g = - 9.8 m/s 2 On way down: v is (-) a g = - 9.8 m/s 2 Speed increases If object returns to height from which it was thrown: (y = y 0 ) then: v = - v 0

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Vertical Motion (not free fall) 1.Objects thrown downward - Initial velocity is NOT zero - Initial velocity is NEGATIVE (“down”)

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Example 1 A book is thrown downward at 5 m/s from a window on the third floor of a high school, which is 10.0 m above the ground. (a)What is the velocity of the book just before it hits the ground? (b)How much time does the book spend in the air before it hits the ground?

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v o = -5 m/s a g = - 9.8 m/s 2 y o = 10 m y = 0 m (a)v = ? (b)t = ? (a) v 2 = v o 2 + 2a(y – y o ) v 2 = (- 5) 2 + 2(- 9.8)(0 – 10) v 2 = 25+ 196 = 221 v = - 14.9 m/s (b) v = v o + at (- 14.9) = (- 5) + (- 9.8)(t) (- 9.9) = (- 9.8)(t) t = 1.01 s

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2. Objects thrown upward - Initial velocity is NOT zero - Initial velocity is POSITIVE (“up”)

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Example 2 A book is thrown upward at 5 m/s from a window on the third floor of a high school, which is 10.0 m above the ground. (a)What is the velocity of the book just before it hits the ground? (b)How much time does the book spend in the air before it hits the ground?

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v o = 5 m/s a g = - 9.8 m/s 2 y o = 10 m y = 0 m (a)v = ? (b)t = ? (a) v 2 = v o 2 + 2a(y – y o ) v 2 = (5) 2 + 2(- 9.8)(0 – 10) v 2 = 25+ 196 = 221 v = - 14.9 m/s (b) v = v o + at -14.9 = 5 + (- 9.8)(t) -19.9 = (- 9.8)(t) t = 2.02 s

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If you drop an object in the absence of air resistance, it accelerates downward at 9.8 m/s 2. If instead you throw it downward, its downward acceleration.

If you drop an object in the absence of air resistance, it accelerates downward at 9.8 m/s 2. If instead you throw it downward, its downward acceleration.

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