Bender, Leela, and Fry are on a treasure Hunt. Bender stole a treasure map from

Question

Bender, Leela, and Fry are on a treasure Hunt. Bender stole a treasure map from a little kid, and they only have a short time to find it before the kid comes back with his parents. Each of them have a meter stick, compass, calculator, and shovel, and scratch down the following displacements in random orders:

69.4 m, 35.0 degrees north of east

47.3 m, 26.0 degrees south of west

16.8 m, due south

(it helps to draw a graph, North=+y axis, East= +x axis)

the three displacement lead to where a sweet bag of loot is buried. Leela and Fry start measuring immediately, but bender, using his mighty Robo-logic, first calculates where to go. what resultant vector does he calculate?

give answer in coordinate and magnitude - angle notation

Explanation / Answer

Fx= 69.4 cos 35 - 47.3 cos 26 = 56.849 - 42,513= 14.336 m

Fy = 69.4 sin 35 - 16.8 - 47.3 sin 26 = 23- 20.735 = 2.265 m

Resultant = 14.336 i + 2.265 j

magnitude = sqrroot ( 14. 336^2 + 2.265^2)= 14.514 m apprx

angle = tan^-1 ( 2.265/ 14.336) = 9 degree aprxfrom +x axis

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