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

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: 72.4 m, 32.0Degree east of north; 57.3 m, 36.0Degree south of west; 17.8 m, due south; (It helps to draw a graph! North = +y axis, East = +x axis) The three displacements 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 your answer in both coordinate and magnitude-angle notation).

Explanation / Answer

Let A = 72.4 m, B = 57.3 m and C = 17.8 m

Ax = 72.4*sin(32) = 38.37 m

Ay = 72.4*cos(32) = 61.4 m

Bx = -57.3*cos(36) = -46.36 m

By = -57.3*sin(36) = -33.68 m

Cy = -17.8 m

Cx = 0

Rx = Ax + Bx + Cx = 38.37 -46.36 + 0 = -7.99 m

Ry = Ay + By + Cy = 61.4 - 33.68 -17.8 = 9.92 m

so, R = (-7.99 i + 9.92 j)m

R = sqrt(Rx^2 + Ry^2)

= sqrt(7.99^2 + 9.92^2)

= 12.74 m

direction : theta = tan^-1(Ry/Rx)

= tan^-1(9.92/-7.99)

= 51.1 degrees north of West

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