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HW01-solutions - smith(js57698 HW01 criss(024809 This...

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smith (js57698) – HW01 – criss – (024809) 1 This print-out should have 18 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 person walks 27 . 0 north of east for 3 . 98 km. Another person walks due north and due east to arrive at the same location. a) How large is the east component of this second path? Correct answer: 3 . 54621 km. Explanation: Δ y Δ x 3 . 98 km 27 Note: Figure is not drawn to scale. Basic Concept: Δ x = d (cos θ ) Given: θ = 27 . 0 d = 3 . 98 km Solution: Δ x = (3 . 98 km)(cos 27 ) = 3 . 54621 km 002 (part 2 of 2) 10.0 points b) How large is the north component of this second path? Correct answer: 1 . 80688 km. Explanation: Basic Concept: Δ y = d (sin θ ) Solution: Δ y = (3 . 98 km)(sin 27 ) = 1 . 80688 km 003 (part 1 of 2) 10.0 points A submarine dives 138 . 0 m at an angle of 17 . 0 below the horizontal. a) What is the horizontal component of the submarine’s displacement? Correct answer: 131 . 97 m. Explanation: Δ y Δ x 138 m 17 Note: Figure is not drawn to scale. Basic Concept: Δ x = d (cos θ ) Given: d = 138 . 0 m θ = 17 . 0 Solution: Δ x = (138 m)[cos( 17 )] = 131 . 97 m 004 (part 2 of 2) 10.0 points b) What is the vertical component of the sub- marine’s displacement? Correct answer: 40 . 3473 m. Explanation: Basic Concept: Δ y = d (sin θ ) Solution: Δ y = (138 m)[sin( 17 )] = 40 . 3473 m 005 (part 1 of 2) 10.0 points A descent vehicle landing on the moon has a vertical velocity toward the surface of the moon of 29 m / s. At the same time, it has a horizontal velocity of 54 . 8 m / s. a) At what speed does the vehicle move along its descent path? Correct answer: 62 . 0003 m / s.
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smith (js57698) – HW01 – criss – (024809) 2 Explanation: v h v v v θ The speeds act at right angles to each other, so v = radicalBig v 2 h + v 2 v = radicalBig (54 . 8 m / s) 2 + (29 m / s) 2 = 62 . 0003 m / s . 006 (part 2 of 2) 10.0 points b) At what angle with the vertical is its path? Correct answer: 62 . 1123 . Explanation: v h is the side opposite and v v is the side adjacent to the angle, so tan θ = v h v v , so θ = arctan bracketleftbigg v h v v bracketrightbigg = arctan bracketleftbigg (54 . 8 m / s) (29 m / s) bracketrightbigg = 62 . 1123 .
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