A roller coaster car moves 239 ft. horizontally and then rises 116 ft. at an ang

Question

A roller coaster car moves 239 ft. horizontally and then rises 116 ft. at an angle of 30° above the horizontal. It then travels 116 ft at an angle of 40° downward. What is the displacement from its starting point? use graphical techniques.
d=___________ft
theta=_________°

11.2 points SerPOP5 1 P037 soln My N A roller-coaster car moves 239 ft horizontally and then rises 116 ft at an angle of 30° above the horizontal. It then travels 116 ft at an angle of 40 downward. What is its displacement from its starting point? Use graphical techniques. (Do this on paper. Your instructor may ask you to turn in this work.) ft o (counterclockwise from the +x-axis)

Explanation / Answer

Given,

x = 239 + [116 cos(30°)] + [116 cos(-40°)] = 428.32 ft

y = [116 sin(30°)] + [116 sin(-40°)]  = -16.56 ft

Displacment, d = (x2 + y2)1/2 = 428.64 ft

tan = (y / x) = (-16.56/ 428.32)
= -2.21°

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