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# solution_pdf3 - chaney(glc568 Vectors and 2D Motion...

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chaney (glc568) – Vectors and 2D Motion – murthy – (21118) 1 This print-out should have 50 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Which of the following are scalar quantities, which are vector quantities? a) velocity. b) age. c) speed. d) acceleration. e) temperature. 1. Vector: velocity; Scalars: age, tempera- ture, speed, acceleration 2. All are vectors. 3. Vectors: velocity, acceleration; Scalars: age, temperature, speed correct 4. Vectors: age, temperature, speed; Scalars: velocity, acceleration 5. All are scalars. Explanation: Speed is a measure of how fast something moves, measured by a unit of distance divided by a unit of time; a scalar quantity. Velocity is specified by describing both speed and the direction of motion; a vector quantity. Age is a measure of how long something exists; a scalar quantity. Acceleration is defined as changes in velocity divided by a certain time interval; a vector quantity since velocity is a vector quantity. Temperature is the quantity that tells how warm or cold an object is with respect to some standard; a scalar. 002 10.0 points Two airplanes leave an airport at the same time. The velocity of the first airplane is 750 m / h at a heading of 52 . 5 . The velocity of the second is 580 m / h at a heading of 90 . How far apart are they after 1 . 3 h? Correct answer: 593 . 863 m. Explanation: Let : v 1 = 750 m / h , θ 1 = 52 . 5 , v 2 = 580 m / h , and θ 2 = 90 . Under constant velocity, the displacement for each plane in the time t is d = v t. These displacements form two sides of a tri- angle with the angle α = θ 2 θ 1 = 37 . 5 between them. The law of cosines applies for ‘SAS’, so the distance between the planes is d = radicalBig d 2 1 + d 2 2 2 d 1 d 2 cos α . Since 2 d 1 d 2 cos α = 2 (975 m) (754 m) cos 37 . 5 = 1 . 16647 × 10 6 m 2 , then d = bracketleftbig (975 m) 2 + (754 m) 2 1 . 16647 × 10 6 m 2 bracketrightbig 1 / 2 = 593 . 863 m . 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. 3. 2. 1. 3. 5. 4. 0. correct 5. 7. Explanation:

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chaney (glc568) – Vectors and 2D Motion – murthy – (21118) 2 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 Two points in the xy plane have cartesian coordinates ( x 1 , y 1 ) and ( x 2 , y 2 ), where x 1 = 7 . 2 m, y 1 = 10 m, x 2 = 10 m, and y 2 = 4 . 5 m. Determine the distance between these points. Correct answer: 22 . 4964 m. Explanation: By simple geometry of triangle, the dis- tance between two points is d = radicalBig [ x 2 x 1 ] 2 + [ y 2 y 1 ] 2 = braceleftbigg bracketleftBig ( 10 m) (7 . 2 m) bracketrightBig 2 + bracketleftBig (4 . 5 m) ( 10 m) bracketrightBig 2 bracerightbigg 1 / 2 = 22 . 4964 m .
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