The route followed by a hiker consists of three displacement vectors a, b, and C

Question

The route followed by a hiker consists of three displacement vectors a, b, and C middot Vector is along a measured trail and is 1840 m in a direction 42.0 degree north of east. Vector B is not along a measured trail, but the hiker uses a compass and knows that the direction is 41.0 0 east of south. Similarly, the direction of vector Q is 39.0 degree north of west. The hiker ends up back where she started, so the resultant displacement is zero, or A + + B + C = 0. Find the magnitudes of (a) vector and (b) vector C. (a) Number Units (b) Number Units

Explanation / Answer

here,

taking north as y axis and east as x axis

A = 1840 * ( cos(42) i + sin(42) j)

A = 1367.39 i + 1231.2 j

B = b * (sin(41) i - cos(41) j )

C = c * ( - cos(39) i + sin(39) j)

A + B + c = 0

1367.39 i + 1231.2 j + b * (sin(41) i - cos(41) j ) + c * ( - cos(39) i + sin(39) j) = 0

equating the vectors

1367.39 + b * sin(41) - c * cos(39) = 0 ....(1)

and

1231.2 - b * cos(41) + c * sin(39) = 0 .....(2)

from (1) and (2)

b = 10465.7 m

c = 10594.5 m

(a)

magnitude of vector b is 10465.7 m

(b)

magnitude of vector c is 10594.7 m

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

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