# 8 - hernandez(ejh742 oldhomework 08 Turner(58120 This...

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hernandez (ejh742) – oldhomework 08 – Turner – (58120) 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 . 3 kg shell with initial ve- locity v i = 8 . 7 m / s in the direction θ = 55 above the horizontal. Δ x Δ h 8 . 7 m / s 55 Δ y y The shell’s trajectory curves downward be- cause of gravity, so at the time t = 0 . 607 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 some data not given in the problem. 2. It depends only on the initial angle θ , and does not depend on the flight time t or the initial velocity v i . 3. It depends on everything: the flight time t , the initial angle θ , and the initial velocity v i . 4. It depends on the initial angle θ and the initial velocity v i , but does not depend on the flight time t . 5. It depends on the flight time t and the initial angle θ , but does not depend on the initial velocity v i . 6. It depends only on the initial velocity v i , and does not depend on the flight time t or the initial angle θ . 7. It depends only on the flight time t , and does not depend on the initial velocity v i or the initial angle θ . correct 8. It depends on the flight time t and the initial velocity v i , but does not depend on the initial angle θ . 9. It is a constant and does not depend on the flight time t or the initial velocity v i or the initial angle θ . 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: 1 . 8054 m.

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hernandez (ejh742) – oldhomework 08 – Turner – (58120) 2 Explanation: Δ h = g t 2 2 = (9 . 8 m / s 2 ) (0 . 607 s) 2 2 = 1 . 8054 m . 003 10.0 points For the ballistic missile aimed to achieve the maximum range of 14500 km, what is the maximum altitude reached in the trajectory? Correct answer: 3625 km. Explanation: For the maximum range R , the launch angle is 45 and the range R is R = v 2 0 sin(2 θ ) g = v 2 0 sin[2 (45 )] g = v 2 0 g .
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