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Homework 3

Homework 3 - homework 03 BAUTISTA ALDO Due 4:00 am Version...

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homework 03 – BAUTISTA, ALDO – Due: Jan 27 2006, 4:00 am 1 Version number encoded for clicker entry: V1:1, V2:4, V3:2, V4:4, V5:3. Question 1 Part 1 of 2. 10 points. A person travels by car from one city to another. She drives for 38 . 9 min at 86 . 2 km / h, 14 . 9 min at 94 . 6 km / h, 35 . 9 min at 37 . 5 km / h, and spends 17 . 1 min along the way eating lunch and buying gas. Determine the distance between the cities along this route. Correct answer: 101 . 816 km (tolerance ± 1 %). Explanation: Distances traveled are x 1 = v 1 t 1 x 2 = v 2 t 2 x 3 = v 3 t 3 Then the total distance traveled is x = x 1 + x 2 + x 3 = (55 . 8863 km) + (23 . 4923 km) + (22 . 4375 km) = 101 . 816 km . Question 2 Part 2 of 2. 10 points. Determine the average speed for the trip. Correct answer: 57 . 2001 km / h (tolerance ± 1 %). Explanation: And, time spent is t = t 1 + t 2 + t 3 + t other = (38 . 9 min) + (14 . 9 min) + (35 . 9 min) + (17 . 1 min) = 1 . 78 h . Hence v av = x t = 101 . 816 km 1 . 78 h = 57 . 2001 km / h . Question 3 Part 1 of 2. 10 points. A runner is jogging at a steady v r = 2 . 9 km / hr. When the runner is L = 7 . 2 km from the finish line a bird begins flying from the runner to the finish line at v b = 14 . 5 km / hr (5 times as fast as the runner). When the bird reaches the finish line, it turns around and flies back to the runner. Even though the bird is a dodo, we will assume that it occupies only one point in space, i.e. , a zero length bird. L v b v r finish line How far does the bird travel? Correct answer: 12 km (tolerance ± 1 %). Explanation: Let, dodo birds fly, and d r be the distance the runner travels. d b be the distance the bird travels. v r be the speed of the runner. v b be the speed of the bird. L = d r be the original distance to the finish line. L 1 be the distance to the finish line after the first encounter. . . . L i be the distance to the finish line after the i th encounter. finish line L 1 d r 1 d b 1 Since the bird travels 5 times as fast as the runner at the first meeting between the bird and runner, d b 1 = 5 d r 1 . (1)

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homework 03 – BAUTISTA, ALDO – Due: Jan 27 2006, 4:00 am 2 The sum of the bird’s and runner’s distances is 5 times L .
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