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Unformatted text preview: pels (kcp389) Homework 2 hill (666) 1 This print-out should have 31 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 (part 1 of 3) 10.0 points A hiker begins a trip by first walking 15 . 5 km southeast from her base camp. On the second day, she walks 43 . 9 km in a direction 74 . 4 north of east, at which point she discovers a forest rangers tower. Determine the y component of the total displacement. Correct answer: 31 . 3227 km. Explanation: Let us denote the displacement vectors on the first and second days by A and B , respec- tively, and use the camp as the origin of the coordinates. Let the angle between A and the positive x direction be , and the angle between B and the positive x direction be . Then we have = 45 , = 74 . 4 . Therefore the components of A are A x = A cos = (15 . 5 km) cos( 45 ) = 10 . 9602 km , A y = A sin = (15 . 5 km) sin( 45 ) = 10 . 9602 km , while the components of B are B x = B cos = (43 . 9 km) cos 74 . 4 = 11 . 8056 km , B y = B sin = (43 . 9 km) sin74 . 4 = 42 . 2828 km . The negative value of A y indicates that the y coordinate had decreased for this displacementin other words, the hiker has walked in the negative y direction. The total displacement R therefore is R = A + B R x = A x + B x = 10 . 9602 km + 11 . 8056 km = 22 . 7657 km R y = A y + B y = 10 . 9602 km + 42 . 2828 km = 31 . 3227 km R = R x i + R y j = 22 . 7657 km i + 31 . 3227 km j Thus, R y = 31 . 3227 km . 002 (part 2 of 3) 10.0 points Find the magnitude of the resultant displace- ment. Correct answer: 38 . 7219 km. Explanation: The magnitude of R is R = radicalBig R 2 x + R 2 y = radicalBig (22 . 7657 km) 2 + (31 . 3227 km) 2 = 38 . 7219 km . 003 (part 3 of 3) 10.0 points Find the angle that the vector R = A + B makes with the positive x axis, use counter- clockwise as the positive angular direction, between the limits of 180 and +180 . Correct answer: 53 . 9899 . Explanation: The inequalities R x = 22 . 7657 km > 0 and R y = 31 . 3227 km > 0 imply that the forest rangers tower is in the first quadrant. Thus, the angle that the vector R = A + B makes with the positive x axis is = arctan R y R x = arctan 31 . 3227 km 22 . 7657 km = 0 . 942301 rad = 53 . 9899 . pels (kcp389) Homework 2 hill (666) 2 004 10.0 points A target lies flat on the ground 11 m from the side of a building that is 10 m tall, as shown below. The acceleration of gravity is 10 m / s 2 . Air resistance is negligible. A student rolls a 11 kg ball off the horizontal roof of the building in the direction of the target....
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