Two beetles run across flat sand, starting at the same point.Beetle 1 runs 0.50
ID: 1665078 • Letter: T
Question
Two beetles run across flat sand, starting at the same point.Beetle 1 runs 0.50 m due east, then 0.88 mat 30° northof due east. Beetle 2 also makes two runs and the first is 1.6 m at48° east ofdue north. (a) What must be the magnitude of its secondrun if it is to end up at the new location of beetle 1?1 m
(b) In what direction must it run?
2° (counterclockwise from due east) (a) What must be the magnitude of its secondrun if it is to end up at the new location of beetle 1?
1 m
(b) In what direction must it run?
2° (counterclockwise from due east)
Explanation / Answer
find the x-position of beetle 1: Rx1=.5cos0+.88cos30=1.26 find how far beetle 2 must run in the x-direction: 1.26=1.6cos(90-48)+x2 x2=.0710m find the y-position of beetle 1: Ry1=.5sin0+.88sin30=.44 find how far beetle 2 must run in the y-direction: .44=1.6sin(90-48)+y2 y2=-.631m Part A) find the magnitude: |R|=(x22+y22)=.635m Part B) use trigonometry to find the angle: =tan-1(y2/x2)=-83.58o remember that the inverse tangent function only gives anglesbetween 90 and -90 (1st and 4th quadrants). so you alwaysneed to look at the components x2 and y2 to see if you found thecorrect angle or if you need to add 180 degrees to it. Sincex2 is positive and y2 is negative, the angle is in the 4thquadrant. add 360 to the angle in order to get it CCW from east: =360-83.58=276.42o