solution4_pdf - arellano(aa39398 Practice Homework 2...

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arellano (aa39398) – Practice Homework 2 Solutions – Weathers – (17101) 1 This print-out should have 24 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 The rectangular and polar coordinates of a point are ( x, y ) and ( r, θ ), where x = 1 and θ = 30 . Determine the value of r . Correct answer: 1 . 1547. Explanation: x = r cos θ r = x cos θ = 1 cos 30 = 1 . 1547 . 002 (part 2 of 2) 10.0 points Determine the value of y . Correct answer: 0 . 577351. Explanation: y = r sin θ = (1 . 1547) sin 30 = 0 . 577351 . 003 10.0 points Which of acceleration, age, speed, tempera- ture, and velocity are vector quantities? 1. Speed and temperature 2. All are vectors. 3. Acceleration and velocity correct 4. Acceleration, age, speed 5. Acceleterion, speed, velocity 6. Age, speed, temperature 7. All are scalars. 8. Acceleration, age, speed, temperature 9. Acceleration, speed, temperature 10. Age and temperature Explanation: Age is a measure of how long something exists; a scalar quantity. Temperature is the quantity that tells how warm or cold an object is with respect to some standard; a scalar quantity. 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. Acceleration is defined as changes in veloc- ity divided by a certain time interval; a vector quantity since velocity is a vector quantity. 004 10.0 points Two airplanes leave an airport at the same time. The velocity of the first airplane is 680 m / h at a heading of 57 . 7 . The velocity of the second is 580 m / h at a heading of 119 . How far apart are they after 2 . 4 h? Correct answer: 1555 . 38 m. Explanation: Let : v 1 = 680 m / h , θ 1 = 57 . 7 , v 2 = 580 m / h , and θ 2 = 119 . 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 = 61 . 3 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 .
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arellano (aa39398) – Practice Homework 2 Solutions – Weathers – (17101) 2 Since 2 d 1 d 2 cos α = 2 (1632 m) (1392 m) cos 61 . 3 = 2 . 18189 × 10 6 m 2 , then d = bracketleftbig (1632 m) 2 + (1392 m) 2 2 . 18189 × 10 6 m 2 bracketrightbig 1 / 2 = 1555 . 38 m . 005 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. 7. 3. 3. 4. 0. correct 5. 5. 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. 006 (part 1 of 2) 10.0 points Consider two vectors vector A and vector B and their re- sultant vector A + vector B . The magnitudes of the vectors vector A and vector B are, respectively, 13 . 8 and 5 . 6 and they act at 57 to each other.
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