Question

In: Physics

You find a pirate map which describes the path to a buried treasure. Starting from an...

  1. You find a pirate map which describes the path to a buried treasure. Starting from an old oak tree in a field, the map instructs you to walk 16.0 meters due west, then turn in the direction 30.0 degrees north of east and walk an additional 21.0 meters. Finally, you need to walk 7.50 meters due south to where the treasure is buried. How far away from the base of the oak tree and in what direction is the treasure buried?

Solutions

Expert Solution

Given,
S1 = 16 m, west
Consider east as along x-axis and north as along y-axis
S1 = - 16 m, east (since west direction is same as negative east direction)
S1 = - 16
S2 = 21 m, 30o north of east
S2 = 21 * cos(30) east + 21 * sin(30) north
= 18.19 m, east + 10.5 m, north.
= 18.19 + 10.5
S3 = 7.5 m, south
= - 7.5 m, north
= - 7.5
Solving for the final displacement
Consider d as the final distance from the oak tree.
S = S1 + S2 + S3
= - 16 + (18.19 + 10.5 ) + (- 7.5 )
= (-16 + 18.19) + (10.5 - 7.5)
= 2.19 + 3
Finding the magnitude of the final diplacement
|d| = SQRT[2.192 + 32]
= SQRT[13.78]
= 3.71 m
Finding the direction of the final diplacement
tanθ = 3/2.19 = 1.37
θ = tan-1(1.37)
= 53.9o
d = 3.71 m, 53.9o north of east.


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