A watermelon has the following coordinates: x = -5.0 m, y =3.0 m, and z =0.0 m.

Question

A watermelon has the following coordinates: x = -5.0 m, y =3.0 m, and z =0.0 m. Find its position vector in terms of the vector's magnitude and orientation. a. Magnitude? b.Angle (in° = deg) as measured counterclockwise from the x-axis . c. Sketch the vector on a right-handed coordinate system. If the watermelon is moved to the x y z coordinates (3.0 m, 0.0 m, 0.0 m), what is its displacement in unit-vector notation? i-component? d. j-component? e. k-component? f. What is its displacement in terms of a magnitude? g. What is its displacement in terms of orientation?

Explanation / Answer

x = -5.0 m, y =3.0 m, and z =0.0 m.

r1=-5i+3j+0k

a)magnitude=?5^2+3^2=5.83

b)dierection with +ve x-axis ?=cos^-1(x/r1)=cos^-1(-5/5.83)=149.05

d)(3.0 m, 0.0 m, 0.0 m)

r2=3i+0j+0k

s=r2-r1=3i+5i-3j=6i+3j

d. j-component?      3.0

e. k-component?      0.0

f. What is its displacement in terms of a magnitude?

s=?3^2+6^2=6.7

g. What is its displacement in terms of orientation?

?=cos^-1(x/s)=cos^-1(6/6.7)=26.42

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