SOL24 - Thevalingam Donald – Homework 24 – Due midnight...

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Unformatted text preview: Thevalingam, Donald – Homework 24 – Due: Mar 26 2007, midnight – Inst: Eslami 1 This print-out should have 8 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 An animal-rescue plane flying due east at 49 m / s drops a bale of hay from an altitude of 52 m . The acceleration due to gravity is 9 . 81 m / s 2 . If the bale of hay weighs 160 N , what is the momentum of the bale the moment it strikes the ground? Correct answer: 953 . 988 kg m / s. Explanation: Let : v plane = 49 m / s , h = 52 m , and W = 160 N . v plane v ⊥ θ 52 m The bale strikes the ground at an angle, so its final velocity v will have both a horizontal and a vertical component, and v 2 = v 2 ⊥ + v 2 h Vertically, conservation of energy gives us E kf = E po 1 2 m v 2 ⊥ = m g h v 2 ⊥ = 2 g h The horizontal component of the bale is v , the speed of the plane, so the speed of the bale as it strikes the ground is v = q v 2 ⊥ + v 2 plane = q 2 g h + v 2 plane The momentum of the bale is thus p = m v = W g q 2 g h + v 2 plane = 160 N 9 . 81 m / s 2 × q 2 (9 . 81 m / s 2 ) (52 m) + (49 m / s) 2 = 953 . 988 kg m / s . 002 (part 2 of 2) 10 points At what angle of inclination will the bale strike? Answer between- 180 ◦ and +180 ◦ . Correct answer: 33 . 0988 ◦ . Explanation: When the bale strikes the ground, the ver- tical component is the side opposite the angle of inclination and the horizontal component is the side adjacent, so tan θ = v ⊥ v plane θ = arctan µ v ⊥ v plane ¶ = arctan µ √ 2 g h v plane ¶ = arctan ˆ p 2 (9 . 81 m / s 2 ) (52 m) 49 m / s !...
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SOL24 - Thevalingam Donald – Homework 24 – Due midnight...

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