Chapter 1: Q24P (page 40)

In Figure $1.59$ , the vector ${\vec{r}}_{1}$ points to the location of object 1 and ${\vec{r}}_{2}$ points to the location of object 2 . Both vectors lie in the $x y$ plane. (a) Calculate the position of object 2 relative to object 1 , as a relative position vector. (b) Calculate the position of object 1 relative to object 2 , as a relative position vector.

Short Answer

Expert verified

(a) Position of object 2 relative to object 1 is: ${\vec{r}}_{2} - {\vec{r}}_{1} = <2, 4, 0>$ m.

(b) Position of object 1 relative to object 2 is: ${\vec{r}}_{2} - {\vec{r}}_{1} = <- 2, - 4, 0>$ m.

Step by step solution

Identification of given data

${\vec{r}}_{1} = <3, - 2, 0> m {\vec{r}}_{2} = <5, 2, 0> m$

Calculating the position of object 2 relative to object 1

(a) To find the position of object 2 relative to object 1 we need first to find their locations relative to the origin, and that is by describing the point where the head of the vectors arrows are located. For object 1, it has the location $<3, - 2, 0>$ m (that's mean ${\vec{r}}_{1} = <3, - 2, 0>$ m), where object 2 is located at (that's mean ${\vec{r}}_{2} = <5, 2, 0>$ m). Now the position of object 2 relative to object 1 is

$∆ \vec{r} = {\vec{r}}_{2} - {\vec{r}}_{1} = <5, 2, 0> - <3, - 2, 0> = <2, 4, 0>$ m.

Calculating the position of object 1 relative to object 2

(b) To find the position of object 1 relative to object 2 we find the do the follow (remember ${\vec{r}}_{1} = <3, - 2, 0>$ m, and $\vec{r_{2}} = <5, 2, 0>$ m).