A
runner travels around a circular track of radius 70 meters. Her speed
is a constant 2m/s. If she runs for 30 minutes,
find total meters moved
first get time in seconds==> 30min*60sec/1min=1800sec
distance=s*t ==> 2m/s*1800s = 3600m
give speed in radians/sec
for this circle, radius = 70m,
so when runner goes 70m, she goes one radian, so...
2m/s*1radian/70m=.03rad/s
find total laps
one lap=one circumference=2pradius==>(2)(p)(70m)=
439.8m
total dist/one lap=total laps....
3600m/(439.8m/lap)= 8.2 laps
OR
51.43radians moved/2pradians
per lap=8.2 laps
find displacement from start point
distance from start is whatever
decimal is left over after the 8th lap.... or
.2 laps
find total radians moved
for this circle, r=70m, so when
traveling along radius if you go 3600m, then you have gone 3600m/70m
=51.43radians
notice that the meters cancel,
leaving us with NO units! We refer to this "natural" way of describing
a circle as a radian
how many degrees did she go total?
51.43radians*57.3degrees/1radian=
2946.7°