Question

While surveying a cave, a spelunker follows a passage 190m straight west, then 210m in a direction 45.0east of south, and then 270m at 30.0 east of north. After a fourth unmeasured displacement, she finds herself back where she started. I need to use vector components to find the magnitude and direction of the fourth displacement.

who can help me solve this?

Answer 1

first consider all the displacements in y direction.

S1 has no displace ment in y direction.
S2 has a displacement of (-210 sin 45)
S3 has a displacement of (270 sin30)

but S1 + S2+ S3+ S4 = 0

0 + (-210 sin 45) + (270 sin30) + Sy=0

Sy= +105 * sqrt2 - 135 = 148.05 -135 = 13.05

similarly consider the displacement in x direction

S1 has a displacement of -190 m
S2 has a displacement of 210 cos45
S3 has a displacement of 270 cos 30
S1 + S2 + S3 + S4 = 0

-190 + 105 * sqrt2 + 135* sqrt3 +S4 = 0

S4 =190 - 148.05 - 233.55= - 191.6

so the final displacement is equal to 191.6i - 13.05j