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Unformatted text preview: cerutti (cpc566) HW02 TSOI (58160) 1 This print-out should have 25 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 car travels 12 . 2 km due north and then 35 . 1 km in a direction = 45 . 2 west of north. A B R x y N E S W Find the magnitude of the cars resultant displacement. Correct answer: 44 . 5458 km. Explanation: Let : A = 12 . 2 km , B = 35 . 1 km , and = 45 . 2 . = 180 - = 180 - 45 . 2 = 134 . 8 , applying the Law of Cosines, R 2 = A 2 + B 2- 2 A B cos . Since- 2 AB cos =- 2 (12 . 2 km)(35 . 1 km) cos134 . 8 = 603 . 477 km 2 , then R = radicalBig (12 . 2 km) 2 + (35 . 1 km) 2 + 603 . 477 km 2 = 44 . 5458 km . 002 (part 2 of 2) 10.0 points Calculate the direction of the cars resul- tant displacement, measured counterclock- wise from the northerly direction. Correct answer: 33 . 9941 . Explanation: Applying the Law of Sines, sin B = sin R sin = B R sin = 35 . 1 km 44 . 5458 km sin134 . 8 = 0 . 559108 = arcsin 0 . 559108 = 33 . 9941 . 003 (part 1 of 2) 10.0 points A river flows at a speed v r = 5 . 36 km / hr with respect to the shoreline. A boat needs to go perpendicular to the shoreline to reach a pier on the rivers other side. To do so, the boat heads upstream at an angle = 39 from the direction to the boats pier. Find the ratio of v b to v r , where v r is defined above and v b is the boats speed with respect to the water. 1. v b v r = sin 2 2. v b v r = tan 3. v b v r = cos 2 4. v b v r = 1 tan 5. v b v r = 1 sin correct 6. v b v r = 1 cos 7. v b v r = 1 cos 2 8. v b v r = sin 9. v b v r = cos cerutti (cpc566) HW02 TSOI (58160) 2 10. v b v r = 1 sin 2 Explanation: Let : v bs =? , boat relative to shore v ws = v r , water relative to shore v bs = v b , boat relative to water . This is a problem about relative velocity. See the figure below. L v bs v b w v ws The velocity of the boat relative to the shore is given by- v bs =- v bw +- v ws . It is easy to see from the figure above that v ws , v bw and v bs form a right triangle if the boat moves northward relative to the earth. Therefore, v ws = v bw sin = v bw v ws = 1 sin . 004 (part 2 of 2) 10.0 points If the time taken for the boat to cross the river is 13 . 9 min, determine the width of the river. Correct answer: 1 . 53342 km. Explanation: By similar reasoning, we know relative to the shore, the velocity of the boat is v bs = v ws tan = 6 . 61905 km / hr . Therefore the time taken for the boat to cross the river is given by t = L v bs = L v ws tan = L tan v ws ....
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- Spring '08