A hiker begins a trip by first walking 25.0 km southeast from her car. She stops

Question

A hiker begins a trip by first walking 25.0 km southeast from her car. She stops and sets up her tent for the night. On the second day, she walks 40.0 km in a direction 60.0° north of east, at which point she discovers a forest ranger’s tower.

(A) Determine the components of the hiker’s displacement for each day.

B) Determine the components of the hiker’s resultant displacement SR for the trip. Find an expression for SR in terms of unit vectors.

C) After reaching the tower, the hiker wishes to return to her car along a single straight line. What are the components of the vector representing this hike? What should the direction of the hike be?

Note: the solutions I've seen all assume a -45 degree angle from the origin by the 25 km vector; how is it automatically known that she travels 25 km -45 degrees from origin?

Explanation / Answer

here,

Part A :
when hker sotheast from her car,
angle = -45 as vector is middle of that quadrant and below horizontal( x axis)
Dx = 25Cos-45 = 17.678 m
Dy = 25Sin45 = -17.678 m

When she walk towards north of east,
Hx = 40*Cos60 = 20 m
Hy = 40*Sin60 = 34.641 m

Part B:
Net displacement in x direction,
x = Dx + Hx = 17.678 + 20 = 37.678 m

Net displacement in y direction,
y = Dy + Hy = -17.678 + 34.641 = 16.963 m

Part C
R = (37.7 i + 16.9 j) ( Rounded off)

direction of hike ,
A = arctan(y/x)
A = arcTan(16.9/37.7)
A = 24.15 degrees

Which towards origin north of east,

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