hw6 - Overton, Mays – Homework 6 – Due: Feb 5 2005,...

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Unformatted text preview: Overton, Mays – Homework 6 – Due: Feb 5 2005, 4:00 am – Inst: Turner 1 This print-out should have 11 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. The due time is Central time. 001 (part 1 of 2) 10 points A cannon fires a 0 . 439 kg shell with initial velocity v i = 9 . 1 m / s in the direction θ = 61 ◦ above the horizontal. The acceleration of gravity is 9 . 8 m / s 2 . Δ x Δ h 9 . 1 m / s 6 1 ◦ Δ y y Shell’s trajectory curves downward because of gravity, so at the time t = 0 . 405 s the shell is below the straight line by some vertical dis- tance. Your task is to calculate this distance Δ h in the absence of air resistance. First, find what does Δ h depend on (be- sides g ): 1. It depends only on the initial velocity v i , and does not depend on the flight time t or the initial angle θ . 2. It depends on the flight time t and the initial angle θ , but does not depend on the initial velocity v i . 3. It is a constant and does not depend on the flight time t or the initial velocity v i or the initial angle θ . 4. It depends only on the flight time t , and does not depend on the initial velocity v i or the initial angle θ . correct 5. It depends only on the initial angle θ , and does not depend on the flight time t or the initial velocity v i . 6. It depends on everything: the flight time t , the initial angle θ , and the initial velocity v i . 7. It depends on the flight time t and the initial velocity v i , but does not depend on the initial angle θ . 8. It depends on the initial angle θ and the initial velocity v i , but does not depend on the flight time t . 9. It depends on some data not given in the problem. Explanation: In the absence of gravity, the shell would fly along the straight line at constant velocity: ˆ x = t v i cos θ , ˆ y = t v i sin θ . The gravity does not affect the x coordinate of the shell, but it does pull its y coordinate at constant downward acceleration a y =- g , hence x = t v i cos θ, y = t v i sin θ- g t 2 2 . Thus, x = ˆ x but y = ˆ y- 1 2 gt 2 , or in other words, the shell deviates from the straight-line path by the vertical distance Δ h = ˆ y- y = g t 2 2 ....
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This note was uploaded on 03/22/2008 for the course PHY 303K taught by Professor Turner during the Spring '08 term at University of Texas at Austin.

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hw6 - Overton, Mays – Homework 6 – Due: Feb 5 2005,...

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