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

$r_{GJ} = r_G - r_j[\tex]now for the above equation we can add the two equations[tex]r_{Gj} = -14\hat i + 36 cos37\hat i - 36sin37\hat j$

$r_{Gj} = 14.75\hat i - 21.67\hat j$

so the magnitude is given as

$r = \sqrt{14.75^2 + 21.67^2} = 26.2 m$

and direction is given as

$\theta = tan^{-1}\frac{21.67}{14.75}= 55.75 degree$

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

Answer 2

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