hw8 - Overton, Mays Homework 8 Due: Feb 10 2005, 4:00 am...

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Overton, Mays – Homework 8 – Due: Feb 10 2005, 4:00 am – Inst: Turner 1 This print-out should have 13 questions. Multiple-choice questions may continue on the next column or page – fnd all choices be±ore answering. The due time is Central time. 001 (part 1 o± 1) 10 points A rowboat crosses a river with a velocity o± 1 . 39 m / s at an angle 36 North o± West relative to the water . 1 . 39 m / s 36 Water’s ±rame o± re±erence Theriveris402mwideandcarriesacurrent o± 2 . 29 m / s due East. W E + - S v s θ s 2 . 29 m / s 402m Shore’s ±rame o± re±erence When the boat reaches the opposite bank, how ±ar East or West (downstream “+” or upstream “ - ”) ±rom its starting point (on the opposite bank) does it land. Note: In your answer, take an Eastward displacement to be positive and a Westward displacement to be negative. Correct answer: 573 . 446 m. Explanation: Let : v b = 1 . 39 m / s , v w = 2 . 29 m / s , θ w = 36 y = 402 m , and θ s = with respect to West v s = with respect to Shore Let the x -axis point East (downstream) and the y -axis point North (across the stream). Let ~v b denote the boat’s velocity relative to the water and ~v w denote the water’s velocity relative to the shore. v b v s v w As shown in the diagram above, the boat’s velocity v s relative to the shore is ~v s = ~v b + ~v w , or in components, v x = v b ( - cos θ w ) + v w = - (1 . 39 m / s)cos(36 ) + (2 . 29 m / s) = 1 . 16547 m / s , v y = v b (sin θ w ) = (1 . 39 m / s)sin(36 ) = 0 . 817022 m / s , so v s = q v 2 x + v 2 y = n (1 . 16547 m / s) 2 + (0 . 817022 m / s) 2 o 1 / 2 = 1 . 42332 m / s θ s = 180 - arctan µ v y v x = 180 - arctan µ 0 . 817022 m / s 1 . 16547 m / s = 144 . 969 . The time it takes the boat to cross the river is t = y v y = (402 m) (0 . 817022 m / s) = 492 . 031 s ,
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Overton, Mays – Homework 8 – Due: Feb 10 2005, 4:00 am – Inst: Turner 2 and during this time, the boat’s downstream displacement is x = tv x = (492 . 031 s)(1 . 16547 m / s) = +573 . 446 m , that is, 573 . 446 m Eastward. 002 (part 1 of 2) 10 points A block is at rest on an incline as shown above. A hand pushes vertically downward with a constant force. Block Which free body diagram for the block best corresponds to this situation? 1. normal weight f hand 2. normal friction weight f hand 3. normal
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hw8 - Overton, Mays Homework 8 Due: Feb 10 2005, 4:00 am...

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