hmwk02 - Su (ycs73) HW02 Tsoi (58020) 1 This print-out...

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Unformatted text preview: Su (ycs73) HW02 Tsoi (58020) 1 This print-out should have 22 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 (part 1 of 2) 10.0 points A person walks the path shown. The total trip consists of four straight-line paths. S N W E 108 m 347m 56 . 2 2 m 2 5 m 29 . Note: Figure is not drawn to scale. a) At the end of the walk, what is the mag- nitude of the persons resultant displacement measured from the starting point? Correct answer: 452 . 392 m. Explanation: d 108 m 347m 124 2 2 m 2 5 m 151 Note: Figure is not drawn to scale. Basic Concepts: x = d (cos ) y = d (sin ) x tot = x 1 + x 3 + x 4 since x 2 = 0 m. y tot = y 2 + y 3 + y 4 since y 1 = 0 m. d = radicalBig ( x tot ) 2 + ( y tot ) 2 Given: d 1 = 108 . 0 m 1 = 0 d 2 = 347 . 0 m 2 = 90 d 3 = 202 . 0 m 3 = 56 . 180 . = 124 d 4 = 250 . 0 m 4 = 180 . 29 . = 151 Solution: x 1 = (108 m)(cos0 ) = 108 m y 2 = (347 m)[cos( 90 )] = 347 m x 3 = (202 m)[cos( 124 )] = 112 . 957 m y 3 = (202 m)[sin( 124 )] = 167 . 466 m x 4 = (250 m)(cos 151 ) = 218 . 655 m y 4 = (250 m)(sin151 ) = 121 . 202 m x tot = 108 m 112 . 957 m 218 . 655 m = 223 . 612 m y tot = 347 m 167 . 466 m + 121 . 202 m = 393 . 263 m and d = radicalBig ( 223 . 612 m) 2 + ( 393 . 263 m) 2 = 452 . 392 m 002 (part 2 of 2) 10.0 points Su (ycs73) HW02 Tsoi (58020) 2 b) What is the direction (measured from due west, with counterclockwise positive) of the persons resultant displacement? Correct answer: 60 . 3772 . Explanation: Basic Concept: tan = y tot x tot Solution: = tan 1 parenleftbigg y tot x tot parenrightbigg = tan 1 parenleftbigg 393 . 263 m 223 . 612 m parenrightbigg = 60 . 3772 south of west. 003 10.0 points A vector of magnitude 3 CANNOT be added to a vector of magnitude 4 so that the magni- tude of the resultant is 1. 1. 2. 3. 3. 5. 4. 7. 5. 0. correct Explanation: The smallest magnitude of the resultant occurs when the vectors are anti-parallel ( R = 1); the largest occurs when they are parallel ( R = 7). Therefore all listed values are possible except R = 0. 004 (part 1 of 2) 10.0 points Consider the motion of a projectile. It is fired at t = 0. The initial velocity vector in rectangular coordinates is v x and v y , and in the polar coordinates is v and (see figure). x y v h R A B The height of the trajectory h, is given by 1. h = v x 2 g . 2. h = 2 g v x 2 . 3. h = v x 2 2 g ....
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hmwk02 - Su (ycs73) HW02 Tsoi (58020) 1 This print-out...

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