A hiker makes four straight-line walks A 30 km at 93 deg B 31 km at 134 deg C 16

Question

A hiker makes four straight-line walks
A 30 km at 93 deg
B 31 km at 134 deg
C 16 km at 94 deg
D 22 km at 164 deg
in random directions and lengths starting at
position (41 km, 41 km) .

Which vector will return the hiker to the
starting point? All angles are measured in a
counter-clockwise direction from the positive
x-axis.
1. = 42.2843 km, 289.899deg
2. = 87.0421 km, 301.414deg
3. = 52.4237 km, 71.8957deg
4. = 28.8273 km, 277.99deg
5. = 43.1569 km, 354.547deg
6. = 54.9212 km, 132.439deg
7. = 27.603 km, 92.1547deg
8. = 58.3758 km, 124.996deg
9. = 11.3817 km, 170.538deg
10.= 33.9896 km, 147.904deg

Explanation / Answer

find the x and y direction of each vector.
Ax = 30sin(93-90) =-1.57 Ay=30cos(93-90) = 29.96
Bx = 31sin(134-90)= -21.53 By=31cos(134-90)=22.30
Cx = 16sin(94-90)= -1.12 Cy=16cos(94-90)=15.96
Dx = 22sin(164-90)=-21.15 Dy= 22cos(164-90)=6.06

Sum of vectors
Vx= -45.37 Vy=74.28
Magnutude =(45.372 + 74.282) =87.04

degree = tan-1(74.28/45.37) = 58.58degree from the negative x-axis

the hiker has travel for 87.04km in the direction 121.42 degree from the positive x-axis.

to travel back, the hiker has to travel 87.04km in the opposite direction.

degree = 121.42 + 180 = 301.42 degree

therefore, the ans is 2.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.