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Test #1-solutions

# Test #1-solutions - Version 026/AABCC – Test#1 –...

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Unformatted text preview: Version 026/AABCC – Test #1 – Antoniewicz – (57420) 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 10.0 points A boat moves through the water of a river at 6 . 15 m / s relative to the water, regardless of the boat’s direction. If the current is flowing at 4 . 96 m / s, how long does it take the boat to complete a trip consisting of a 466 m displacement down- stream followed by a 258 m displacement up- stream? 1. 114.56 2. 46.735 3. 93.1923 4. 219.116 5. 75.8412 6. 258.751 7. 65.944 8. 161.11 9. 110.486 10. 77.0348 Correct answer: 258 . 751 s. Explanation: Let v b be the velocity of the boat relative to the water, and v w the velocity of water relative to the shore. Take downstream as the positive direction. For the downstream trip, the current is speeding him up, so the velocity of the boat relative to the shore is v d = v b + v w and the time is t d = x d v d = x d v b + v w For the upstream trip, the current is slowing him down, so the velocity of the boat relative to the shore is v u = v b − v w and the time is t u = x u v u = x u v b − v w The time for the entire trip is thus t = t d + t u = x d v b + v w + x u v b − v w = (466 m) (6 . 15 m / s) + (4 . 96 m / s) + (258 m) (6 . 15 m / s) − (4 . 96 m / s) = 258 . 751 s 002 (part 1 of 3) 4.0 points A motorboat heads due east at 13 . 4 m/s across a river that flows toward the south at a speed of 4 . 8 m/s. a) What is the magnitude of the resultant velocity relative to an observer on the shore? 1. 11.3217 2. 14.7258 3. 13.9014 4. 15.7166 5. 15.2555 6. 11.5694 7. 15.426 8. 12.7389 9. 11.7004 10. 14.2338 Correct answer: 14 . 2338 m / s. Explanation: 13 . 4 m / s 4 . 8m / s v be θ Note: Figure is not drawn to scale. Basic Concepts: vectorv be = vectorv br + vectorv re Since the velocities are perpendicular, v 2 be = v 2 br + v 2 re Given: Let north and east be positive: v br = 13 . 4 m / s v re = − 4 . 8 m / s Version 026/AABCC – Test #1 – Antoniewicz – (57420) 2 Solution: v be = radicalBig (13 . 4 m / s) 2 + ( − 4 . 8 m / s) 2 = 14 . 2338 m / s 003 (part 2 of 3) 3.0 points b) What is the angle from the original heading (with counterclockwise positive) of the boat’s displacement? 1. -19.2419 2. -12.6996 3. -18.5502 4. -19.708 5. -24.4867 6. -16.7712 7. -18.1595 8. -20.1363 9. -15.4359 10. -16.1645 Correct answer: − 19 . 708 ◦ ....
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Test #1-solutions - Version 026/AABCC – Test#1 –...

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