In: Physics
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?
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.