Question

John, paul, and george are standing in a strawberry field. paul is 14.0 m due west of john. george is 36.0 m from paul, in a direction 37.0° south of east from paul's location. how far is george from john? what is the direction of george's location from that of john?

Answer 1

Position of paul with respect to john is given as

14 m due west of john

`r_(pj) = r_p - r_j = -14\hat i`

position of George with respect to Paul is given as 36 m in direction 37 degree south of east

`r_(GP) = r_G - r_p = 36cos37\hat i - 36 sin37\hat j`

now we need to find the position of George with respect to John

`r_(GJ) = r_G - r_j[\tex]</p><p>now for the above equation we can add the two equations</p><p>[tex]r_(Gj) = -14\hat i + 36 cos37\hat i - 36sin37\hat j`

`r_(Gj) = 14.75\hat i - 21.67\hat j`

so the magnitude is given as

`r = √(14.75^2 + 21.67^2) = 26.2 m`

and direction is given as

`\theta = tan^(-1)(21.67)/(14.75)= 55.75 degree`

so it is 26.2 m at an angle 55.75 degree South of east