hw 6 - homework 06 – HETTIGER CHRISTOF – Due 4:00 am 1...

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Unformatted text preview: homework 06 – HETTIGER, CHRISTOF – Due: Jan 31 2008, 4:00 am 1 Question 1, chap 3, sect 1. part 1 of 1 10 points A quarterback takes the ball from the line of scrimmage, runs backward for 11 yards, then runs sideways parallel to the line of scrim- mage for 18 yards. At this point, he throws a 23 yards forward pass straight downfield perpendicular to the line of scrimmage. What is the magnitude of the football’s resultant displacement? Correct answer: 21 . 6333 yards (tolerance ± 1 %). Explanation: Let the x direction be parallel to line of scrimmage. Given : ∆ y 1 = − 11 yards , ∆ x = ± 18 yards , and ∆ y 2 = 23 yards . ∆ y tot = ∆ y 1 + ∆ y 2 = − 11 yards + 23 yards = 12 yards ∆ x tot = ∆ x = ± 18 yards The displacements are perpendicular, so d = radicalBig (∆ x tot ) 2 + (∆ y tot ) 2 = radicalBig ( ± 18 yards) 2 + (12 yards) 2 = 21 . 6333 yards . Question 2, chap 3, sect 3. part 1 of 5 10 points A commuter airplane starts from an air- port located at the origin (see figure). First it flies to city “A” located a = 120 km away from the airport in a direction α = 39 ◦ North of East. Next it flies b = 56 . 5 km β = 38 ◦ West of North to city “B”. Finally it flies c = 178 km due West to city “C”. A B C O a c b r α β γ N N E W Consider “E” to be the positive x axis and “N” to be the positive y axis. Which of the following is equal to the x- component b x of the vector vector b ? 1. b x = b cos β 2. b x = − b tan β 3. b x = − b sin β correct 4. b x = − b cos β 5. b x = b sin β 6. b x = b tan β Explanation: Let : b = 56 . 5 km β = 38 ◦ Basic Concepts: The rule for adding two vectors vectorv = ( v x ,v y ) and vectoru = ( u x ,u y ) is vectorr = vectoru + vectorv = ( v x + u x ,v y + u y ) thus vector components add. Solution b β | b x | | b y | Here β is defined as the angle between vector b and a vertical line. Also, for β < 90 ◦ ( as in this problem), vector b is in the 2 nd quadrant, i.e. its x component is negative and its y component positive. b x = − b sin β homework 06 – HETTIGER, CHRISTOF – Due: Jan 31 2008, 4:00 am 2 = − (56 . 5 km) sin38 ◦ = − 34 . 7849 km . Question 3, chap 3, sect 3. part 2 of 5 10 points Which of the following is equal to the y- component b y of the vector vector b ? 1. b y = b tan β 2. b y = − b tan β 3. b y = − b sin β 4. b y = b cos β correct 5. b y = − b cos β 6. b y = b sin β Explanation: Let : b = 56 . 5 km β = 38 ◦ b y = b cos β = (56 . 5 km) cos(38 ◦ ) = 44 . 5226 km Question 4, chap 3, sect 3. part 3 of 5 10 points What is the x-component r x of vector vector r from the starting point, position “O”, to the city “C” in km?...
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hw 6 - homework 06 – HETTIGER CHRISTOF – Due 4:00 am 1...

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