As preparation for this problem, consult Concept Simulation 1.1. On a safari, a
ID: 1773725 • Letter: A
Question
As preparation for this problem, consult Concept Simulation 1.1. On a safari, a team of naturalists sets out toward a research station located 5.53 km away in a direction 31.9 ° north of east. After traveling in a straight line for 1.82 km, they stop and discover that they have been traveling 18.8 ° north of east, because their guide misread his compass. What are (a) the magnitude and (b) the direction (as a positive angle relative to due east) of the displacement vector now required to bring the team to the research station?
Explanation / Answer
The starting point will be at the origin, O = (0, 0).
The vector to the research station will be
S = (5.53*cos(31.9), 5.53*sin(31.9))
The vector that described the team's actual movement will be
T = (1.82*cos(18.8), 1.82*sin(18.8))
To find their new course, N, we subtract where they are now, T, from where they want to be, S.
N = S - T
N = (Sx - Tx, Sy - Ty)
N = [(5.53*cos(31.9) - 1.82*cos(18.8)), ( 5.53*sin(31.9) - 1.82*sin(18.8))]
N = [ 2.97, 2.34] = (Nx, Ny)
The magnitude of vector N is
N = sqrt((Nx)^2 + (Ny)^2)
N = 3.78 m
The direction is tan^-1(Ny / Nx)
theta = tan^-1(2.34 / 2.97) = 38.2 degree.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.