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Unformatted text preview: toledo (gt4725) hwk 1 metaxas (16111) 1 This print-out should have 18 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. Homework 1 is based on chapter 2. It is due on Monday 1/31/11 at midnight and consists of 10 questions. It will say it is due at 2am on Tuesday, but the computer is in Texas and 2am there is midnight of the previous day here. 001 (part 1 of 2) 10.0 points A runner is jogging at a steady 5 . 2 km / hr. When the runner is 7 . 9 km from the finish line, a bird begins flying from the runner to the finish line at 15 . 6 km / hr (3 times as fast as the runner). When the bird reaches the finish line, it turns around and flies back to the runner. L v b v r finish line How far does the bird travel? Even though the bird is a dodo, assume that it occupies only one point in space (a zero length bird) and that it can turn without loss of speed. Correct answer: 11 . 85 km. Explanation: Let : v r = 5 . 2 km / hr , L = 7 . 9 km , and v b = 3 v r . finish line L 1 dr 1 db 1 The runner travels a distance x until the encounter with the bird. In that time, the bird has traveled a distance L +( L- x ) = 2 L- x . The bird travel 3 times as fast as the runner during this time frame, so d b = 3 d r 2 L- x = 3 x 2 L = 4 x x = 1 2 L and the bird flies a distance of d b = 2 L- 1 2 L = 3 2 L = 3 2 (7 . 9 km) = 11 . 85 km . 002 (part 2 of 2) 10.0 points After this first encounter, the bird then turns around and flies from the runner back to the finish line, turns around again and flies back to the runner. The bird repeats the back and forth trips until the runner reaches the finish line. How far does the bird travel from the be- ginning (including the distance traveled to the first encounter)? Correct answer: 23 . 7 km. Explanation: The distance remaining for the runner after the first encounter is L 1 = 1 2 L , and again the bird will fly 3 times as far as the runner until the next encounter. This pattern repeats over the entire original distance, so d b = 3 L = 3 (7 . 9 km) = 23 . 7 km . 003 (part 1 of 2) 10.0 points A speedy tortoise can run at 0 . 08 m / s, and a hare can run 19 times as fast. In a race, they start at the same time, but the hare stops to rest for 2 . 2 min, so the tortoise wins by a shell (20 cm). How long does the race take? Correct answer: 139 . 194 s. toledo (gt4725) hwk 1 metaxas (16111) 2 Explanation: Let : v t = 0 . 08 m / s , v h = 19 v t , = 2 . 2 min , and = 0 . 2 m ....
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