Question

2. Treasure Hunt. The treasure map below comes with the following instructions: Start at the tree and walk due north for 500 paces, then due east for 100 pages. Dig. X- Treasure a. What are the coordinates of the treasure? Express your answer as a vector i written in component form. Angry Dragon 60° Yellow brick road Tree You'd like to follow the instructions, but there's an angry dragon exactly north of the tree, To avoid the dragon, you instead walk along the yellow brick road at an angle 60° as indicated on the map for 300 paces and arrive at location A. b. Define a vector A that represents your path along the yellow brick road. Express this vector in component form. c. In which direction and how far should you walk to now reach the treasure from point A?

Answer 1

a)

(x, y) = (100,500)

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b)

Ax = 300 sin 60 = 59

Ay = 300 cos 60 = 150

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c)

net horizontal compo

Rx = 59 +100 = - 41

net vertical compo

Ry = 500 - 150 = 350

displacement need to cover

R^2 = Rx^2 + Ry^2

R = 532.4 pace

direction

x = arctan ( 350 / 41) = 83.32 above west