Two beetles run across flat sand, starting at the same point.Beetle 1 runs 0.50
ID: 1665254 • Letter: T
Question
Two beetles run across flat sand, starting at the same point.Beetle 1 runs 0.50 m due east, then 0.90 m at 28° north of dueeast. Beetle 2 also makes two runs and the first is 1.6 mat 48° east of due north. (a) What must be the magnitude of its second run if it is to end upat the new location of beetle 1?m
(b) In what direction must it run?
°(counterclockwise from due east) (a) What must be the magnitude of its second run if it is to end upat the new location of beetle 1?
m
(b) In what direction must it run?
°(counterclockwise from due east)
Explanation / Answer
in the given problem let Arepresent the first part of the beetles 1's trip (0.50 m east or0.5 i^) C represent the first part ofthe beetles 2's trip intended voyage (1.6 m at 48o northof east). for the respective second parts B is 0.90 m at 28onorth of east D is unknown A + B = 0.5 i^+ 0.90 (cos28o i^ + sin28o j^) = ...... i^ + ...... j^ the equation relating these will be A + B =C + D where C = 1.60 (cos48o i^+ sin48o j^) = ...... i^ + ......j^ (a) D = A +B - C magnitude D = ..... m (b) the angle will be = tan-1(- ...../ 0.16) = ......o which is interpreted to mean south of east or90- east of south