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PHYS 111 LAB and HW

PHYS 111 LAB and HW - ghei(mg42382 HW 1 Opyrchal(11130 This...

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ghei (mg42382) – HW 1 – Opyrchal – (11130) 1 This print-out should have 10 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points A hiker makes four straight-line walks A 24 km at 45 B 11 km at 319 C 24 km at 97 D 15 km at 157 in random directions and lengths starting at position (41 km , 41 km) , A B C D How far from the starting point is the hiker after these four legs of the hike? All angles are measured in a counter-clockwise direction from the positive x -axis. Correct answer: 40 . 3501 km. Explanation: Let : ( x 0 , y 0 ) = (41 km , 41 km) . Δ a x = (24 km) cos 45 = 16 . 9706 km , Δ a y = (24 km) sin 45 = 16 . 9706 km , Δ b x = (11 km) cos 319 = 8 . 30182 km , Δ b y = (11 km) sin 319 = 7 . 21663 km , Δ c x = (24 km) cos 97 = 2 . 92488 km , Δ c y = (24 km) sin 97 = 23 . 8211 km , Δ d x = (15 km) cos 157 = 13 . 8076 km , Δ d y = (15 km) sin 157 = 5 . 86095 km , A B C θ e D E Scale: 10 km = Δ x = Δ a x + Δ b x + Δ c x + Δ d x = 16 . 9706 km + (8 . 30182 km) + 2 . 92488 km + ( 13 . 8076 km) = 8 . 53992 km and Δ y = Δ a y + Δ b y + Δ c y + Δ d y = 16 . 9706 km + ( 7 . 21663 km) + 23 . 8211 km + (5 . 86095 km) = 39 . 436 km , so the resultant is E = radicalBig x ) 2 + (Δ y ) 2 = radicalBig (8 . 53992 km) 2 + (39 . 436 km) 2 = 40 . 3501 km . 002 (part 1 of 2) 10.0 points A particle undergoes two displacements, mea- sured from the positive x -axis, with counter- clockwise positive. The first has a magnitude of 11 m and makes an angle of 70 with the positive x axis. The resultant displacement has a magnitude of 8 . 2 m directed at an angle of 102 from the positive x axis.
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