Two beetles run across flat send, starting at the same point. Beetle 1 runs `0.50` m due east, the `0.80` m at `30^(@)` north of due east. Beetle 2 also makes two runs, the first is `1.6m` at `40^(@)` east of due north. What must be (a) the magnitude and (b) the direction of its second run if it is to end up at the new location of beetle 1 ?

Explanation

(a) We find `vecD= vecA + vecB-vecC=(0.16m) hati + (-0.83m) hatj,and ` the magnituide is `D=0.84m.`
(b) The angle is `tan ^(-1) (-0.83//0.16)=-79^(@)` which is interpreted tomean `79^(@)` south of east (or `11^(@)` east of south).