A hiker begins a trip by first walking 23.0 km southeast from her base camp. On

Question

A hiker begins a trip by first walking 23.0 km southeast from her base camp. On the second day she walks 36.0 km in a direction 60.0 degrees north of east, at which point she discovers a forest ranger's tower. (A) Determine the components of the hiker's displacements in the first and second days. Ax = ? km. Ay = ? km. Bx = ? km. By = ? km. (B) Determine the components of the hiker's total displacement for the trip. Rx = ? km. Ry = ? km. (C) Find the magnitude and direction of the displacement from base camp. Magnitude, ? km. Direction, ? Degrees north of east.

Explanation / Answer

A)

the component of the hiker's displacement for first day is,

Ax=A*cos(-theta)

Ax=23*cos(-45)=16.26km

Ay=A*sin(-theta)

Ay=23*sin(-45)=-16.26km

and

the component of the hiker's displacement for second day is,

Bx=B*cos(theta)

Bx=36*cos(60)=18km

By=B*sin(theta)

By=36*sin(60)=31.17km

B)

the resultant displacemenet,

Rx=Ax+Bx

Rx=16.26+18

RX=34.26 km

and

Ry=Ay+By

Ry=(-16.26)+(31.17)

Ry=14.91km

therefore,

R=(Rx)i+(Ry)j

R=(34.26)i+(14.91)j

C)

magnitude of R=sqrt(34.26^2+14.91^2)

R=37.36km

and

direction, tan(theta)=Ry/Rx

tan(theta)=14.91/34.26

===> theta=23.51 degrees north of east

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