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Unformatted text preview: Create assignment, 18042, Homework 3, Jul 29 at 1:14 pm 1 This print-out should have 11 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. The due time is Central time. Wind and a Jet 01 03:04, trigonometry, numeric, < 1 min, nor- mal. 001 A jet airliner moving initially at 300 mph (with respect to the ground) to the east moves into a region where the wind is blowing at 100 mph in a direction 30 ◦ north of east. What is the new speed of the aircraft with respect to the ground? Correct answer: 389 . 822 mph. Explanation: V wind V V jet θ The new velocity of the aircraft is the sum of the initial velocity and the velocity of the wind: ~v f = ~v i + ~v wind = v x ˆ ı + v y ˆ where v x = v i + v wind cos θ v y = v wind sin θ so the speed is | ~v | = q v 2 x + v 2 y . Bee in the Wind 04:06, trigonometry, numeric, > 1 min, nor- mal. 002 A bee flies to a flower 557 m due south of its hive. The bee’s speed in still air is 0 . 71 m / s, and there is a wind blowing toward the south at 0 . 23 m / s. How long will it take the bee to travel to the flower and back to the hive? Correct answer: 1752 . 97 s. Explanation: The wind helps the bee fly faster on the downwind trip than on the return trip. The time to go to the flower is given by t with = s with v with = s v bee + v wind The wind slows the bee on the return trip, so the time for the return trip is t against = s against v against = s v bee- v wind The total time is t = t with + t against Crossing a River 02 04:06, calculus, numeric, > 1 min, normal. 003 A river flows at a speed v r = 5 km / hr with respect to the shoreline. A boat needs to go perpendicular to the shoreline to reach a pier on the river’s other side. To do so, the boat heads upstream at an angle θ = 30 ◦ from the direction to the boat’s pier....
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