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Chapter_2_and_3_09 - Chapter 2 Problems 2.58 A rock is...

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Chapter 2 Problems 2.58 A rock is thrown vertically uward from ground level at time t=0. At t=1.5s, it passes the to of a tall tower and 1.0 s later, it reaches its maximum height. What is the height of the tower t=1.5s t=2.5s t=0 s y 1.5 =h y 2.5 We begin by considering the t=0 to t=1.5s part of the trip. y i = 0 m y 1.5 = h v i = ? v 1.5 = ? a =- g t = 1.5 s We can find the height if we have the initial velocity, using y 1.5 = y i + v i t + 2 1 a t 2 To find the initial velocity, we consider the entire 2.5 second trip.
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y i = 0 m y 2.5 = ? v i = ? v 2.5 = 0 a =- g t = 2.5 s v 2.5 = v i - g $ 2.5 s v i = g $ 2.5 s = 24.5 m / s Now that we know the initial velocity, we can find the height of the tower. y 1.5 = y i + v i t + 2 1 a t 2 y 1.5 = y i + 24.5 m / s $ 1.5 s - 2 1 $ 9.8 m / s 2 $ (1.5 s ) 2 = 25.725 m 2.67 How far does the runner whose velocity-time graph is shown in Fig 2036 travel in 16 s? The figure’s vertical scaling is et by v s =8.0m/s The runner’s displacement is the area under the curve. We can compute the area geometrically A = 2 1 $ 2 s $ 8 m / s + 8 s $ 8 m / s + 2 1 $ 2 s $ 4 m / s + 2 s $ 4 m / s + 4 s $ 4 m / s = 100 m 2.108 A ball is thrown vertically downward from the top of a 36.6m tall building. The ball passes the top of a window that is 12.2m above the ground 2.00s after being thrown. What is the speed of the ball as it passes the top of the window? t=0s t=2.0 s y i =36.6m y f =12.2m Once again, we write what we know
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y i = 36.6 m y f = 12.2 m v i = ? v f = ? a =- g t = 2.0 s As in the previous problem, we need the initial velocity to find the result that we are looking for --in this case the final velocity. We can find the initial velocity y f = y i + v i t + 2 1 a t 2 = y i + v i t - 2 1 g t 2 v i = t y f - y i + 2 1 g t 2 =-2.4 m / s We can now find the final velocity v f = v i + at =-2.4 m / s - 9.8 m / s 2 $ 2 s =-22 m / s Chapter 3 Problems 3.1 The x component of a certain vector is -25.0 units and the y component is +40 units. (a) What is the magnitude and direction of the vector?
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