Hw 2 Solutions

# Hw 2 Solutions - Bell Evan – Homework 2 – Due 11:00 pm...

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Unformatted text preview: Bell, Evan – Homework 2 – Due: Jan 26 2005, 11:00 pm – Inst: Furlan 1 This print-out should have 20 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. The due time is Central time. 001 (part 1 of 1) 10 points A person walks 25 m west and then 45 m at an angle of 60 ◦ north of east. What is the magnitude of the total dis- placement? 1. 43.6 m 2. 31.0 m 3. 39.1 m correct 4. 67.8 m 5. 26.5 m 6. 60.2 m 7. 45.7 m 8. 56.3 m 9. 40.9 m 10. 61.4 m Explanation: In a triangle with three sides of a, b, and c , if the angle between a and b is θ , then c 2 = a 2 + b 2- 2 ab cos θ . 002 (part 1 of 1) 10 points An airplane flies 330 km due east, makes a right-angle turn, and then flies 390 km due north. Find the magnitude of the plane’s displace- ment from its starting point. (Neglect the curvature of the earth.) Correct answer: 510 . 882 km. Explanation: The displacements are at right angle to each other, so the resultant is the hypotenuse of a right triangle and r 2 = x 2 + y 2 r = p x 2 + y 2 003 (part 1 of 1) 10 points A person walks 37 m East and then walks 33 m at an angle 22 ◦ North of East. What is the magnitude of the total dis- placement? Correct answer: 68 . 7181 m. Explanation: The total displacement is the vector sum of the two displacements, so R x = R a + R b cos θ = 37 m + 33 mcos22 ◦ = 67 . 5971 m R y = R b sin θ = 33 msin22 ◦ = 12 . 362 m The final displacement is R = q R 2 x + R 2 y = q (67 . 5971 m) 2 + (12 . 362 m) 2 = 68 . 7181 m . 004 (part 1 of 1) 10 points An ant starts at one edge of a long strip of paper that is 34 . 5 cm wide. She travels at 1 . 7 cm / s at an angle of 53 ◦ with the long edge. How long will it take her to get across? Correct answer: 25 . 411 s. Explanation: d θ v Although her velocity is 1 . 7 cm / s, she ad- vances toward her goal (the opposite edge) at less than this speed. In fact, her actual speed is the hypotenuse of a right triangle, and the rate at which she approaches the opposite edge is defined by v ⊥ = v sin θ . Thus, her time is given by t = d v ⊥ = 34 . 5 cm (1 . 7 cm / s) sin53 ◦ = 25 . 411 s Bell, Evan – Homework 2 – Due: Jan 26 2005, 11:00 pm – Inst: Furlan 2 005 (part 1 of 2) 10 points A roller coaster travels 161 ft at an angle of 37 . 8 ◦ above the horizontal. How far does it move horizontally? Correct answer: 127 . 215 ft. Explanation: Basic Concepts Horizontal displacement is x = a cos θ and vertical displacement y = a sin θ . Solution Moving for 161 ft at an angle of 37 . 8 ◦ above the horizontal moves the roller coaster along the horizontal a distance x given by x = (161 ft)(cos37 . 8 ◦ ) = 127 . 215 ft 006 (part 2 of 2) 10 points How far does it move vertically?...
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Hw 2 Solutions - Bell Evan – Homework 2 – Due 11:00 pm...

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