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H Hautelook Course Home MasteringPhysics Masteringprys x c o ·secure https://session.masteringphysics.com/myc 91698745&offset-ne; Problem 3.40 - Enhanced-with Video Solution The treasure map in the figure gives the following directions to the buried treasure: "Start at the old oak tree, walk due north for 450 paces, then due east for 150 paces. Dig. But when you arrive, you find an angry dragon just north of the tree. To avoid the dragon, you set off along the yellow brick road at an angle 60° east of north. After walking 340 paces you see an opening through the woods. (Figure 1) Part A Which direction should you go to reach the treasure? 0? You may want to review (Page 65) For help with math skills, you may want to review For general problem-solving tips and strategies for this topic, you may want to view a Video Tutor Solution o Part B Figure 1 of 1 How far should you go to reach the treasure? × Treasure paces Submit Request Answer Yellow brick road Tree Provide Feedback

Explanation / Answer

Part A -

Consider, due north is the positive y-direction
and due east is the positive x-direction

So, the location that you want to arrive at is: (150, 450)

Now, use the alternate path:
X: 340 cos (90 - 60) = 294.4
Y: 340 sin (90 - 60) = 170.0

therefore, to reach treasure, you will need to travel a distance of:
D^2 = (150 - 294.4)^2 + (450 - 170.0)^2

=> D^2 =  20851.36 + 78400 = 99251.36

=> D = 315 paces

Part B -

Direction:
Tan (theta) = (Y/X)
theta = arctan(Y/X)
theta = arctan(280 / -144.4)
theta = -62.72 deg* or 62.72 deg. North of West

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