Problem: Find vector components, given a magnitude and direction, and vice Versa

Question

Problem: Find vector components, given a magnitude and direction, and vice Versa.(A) Find the horizontal and vertical components of the r = 1.08 X 10 (to the second power) m displacement of a superhero who flies from the top of a tall building along a path downward at a 30.0 degree angle on the x y coordinates and having gone 100 m. Horizontal, ? m. Vertical, ? m. (B) Suppose instead the superhero leaps in the other direction along a displacement vector B (half arrow over B), to the top of a flagpole where the displacement components are given by Bx = 24.0 m and By = 11.4 m. Find the magnitude and direction of the displacement vector. Magnitude, ? m. Direction, ? Degrees.

Explanation / Answer

let,

r=1.08*10^2 m

a)

horizontal component,

Ax=r*cos(-theta)

Ax=1.08*10^2*cos(-30)

Ax=93.53 m

and

vertical component,

Bx=r*sin(theta)

Bx=1.08*10^2*sin(-30)

Bx=-54 m

b)

Bx=24m, By=11.4m

magnitude B=sqrt(Bx^2+By^2)

B=sqrt(24^2+11.4^2)

direction, tan(theta)=Ay/Ax

tan(theta)=11.4/24

===> theta=25.41 degrees

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