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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 xcomponent r x of vector vector r from the starting point, position “O”, to the city “C” in km?...
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 Spring '10
 Turner
 Physics, Vector Space, Force, Work, Euclidean vector, F3

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