Homework #4 Vectors, Horizontal Projectiles-solutions

# Homework #4 Vectors, Horizontal Projectiles-solutions -...

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Unformatted text preview: sanchez (es25396) – Homework #4 Vectors, Horizontal Projectiles – guevara – (130101) 1 This print-out should have 12 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points A person walks 30 m East and then walks 35 m at an angle 47 ◦ North of East. What is the magnitude of the total dis- placement? Correct answer: 59 . 6422 m. Explanation: The total displacement is the vector sum of the two displacements, so R x = R a + R b cos θ = 30 m + 35 m cos 47 ◦ = 53 . 8699 m R y = R b sin θ = 35 m sin 47 ◦ = 25 . 5974 m The final displacement is R = radicalBig R 2 x + R 2 y = radicalBig (53 . 8699 m) 2 + (25 . 5974 m) 2 = 59 . 6422 m . 002 (part 1 of 2) 10.0 points Given two vectors vector F 1 , and vector F 2 . Where the magnitude of these vectors are F 1 = 78 N , and F 2 = 56 N . And where θ 1 = 27 ◦ , and θ 2 = 78 ◦ . The angles are measure from the positive x axis with the counter-clockwise angular direc- tion as positive. What is the magnitude of the resultant vec- tor bardbl vector F bardbl , where vector F = vector F 1 + vector F 2 ? Correct answer: 121 . 317 N. Explanation: Drawing a diagram to scale of the vectors, we have θ F 1 F 2 F Scale: 10 N where : F 1 = 78 N , θ 1 = 27 ◦ , F 1 x = 69 . 4985 N , F 1 y = 35 . 4113 N , F 2 = 56 N , θ 2 = 78 ◦ , F 2 x = 11 . 6431 N , F 2 y = 54 . 7763 N , and F = 121 . 317 N , θ = 48 . 0223 ◦ , F x = 81 . 1416 N , F y = 90 . 1875 N ....
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Homework #4 Vectors, Horizontal Projectiles-solutions -...

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