# hw8 - lenoir(wml297 – oldhomework 08 – Turner –(58220...

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Unformatted text preview: lenoir (wml297) – oldhomework 08 – Turner – (58220) 1 This print-out should have 14 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 (part 1 of 2) 10.0 points A cannon fires a 0 . 221 kg shell with initial velocity v i = 9 m / s in the direction θ = 48 ◦ above the horizontal. Δ x Δ h 9 m / s 4 8 ◦ Δ y y The shell’s trajectory curves downward be- cause of gravity, so at the time t = 0 . 414 s the shell is below the straight line by some verti- cal distance Δ h . Your task is to calculate the distance Δ h in the absence of air resistance. On what does Δ h depend (besides g )? 1. It depends on the initial angle θ and the initial velocity v i , but does not depend on the flight time t . 2. It depends only on the initial velocity v i , and does not depend on the flight time t or the initial angle θ . 3. It depends on the flight time t and the initial angle θ , but does not depend on the initial velocity v i . 4. It depends on the flight time t and the initial velocity v i , but does not depend on the initial angle θ . 5. It depends only on the flight time t , and does not depend on the initial velocity v i or the initial angle θ . correct 6. It depends only on the initial angle θ , and does not depend on the flight time t or the initial velocity v i . 7. It depends on everything: the flight time t , the initial angle θ , and the initial velocity v i . 8. It is a constant and does not depend on the flight time t or the initial velocity v i or the initial angle θ . 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 . Note that this result is completely indepen- dent on the initial velocity v i or angle θ of the shell. It is a simple function of the flight time t and nothing else (besides the constant g = 9 . 8 m / s 2 ). 002 (part 2 of 2) 10.0 points Find the Δ h . The acceleration of gravity is 9 . 8 m / s 2 . Correct answer: 0 . 83984 m. lenoir (wml297) – oldhomework 08 – Turner – (58220) 2 Explanation: Δ h = g t 2 2 = (9 . 8 m / s 2 ) (0 . 414 s) 2 2 = . 83984 m . 003 10.0 points For the ballistic missile aimed to achieve the maximum range of 17500 km, what is the maximum altitude reached in the trajectory?...
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## This note was uploaded on 04/15/2010 for the course PHY 12343 taught by Professor Turner during the Spring '10 term at University of Texas.

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hw8 - lenoir(wml297 – oldhomework 08 – Turner –(58220...

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