Marla is running clockwise around a circular track. She runs at a constant speed
ID: 2911547 • Letter: M
Question
Marla is running clockwise around a circular track. She runs at a constant speed of 3 meters per second. She takes 58 seconds to complete one lap of the track. From her starting point, it takes her 12 seconds to reach the northernmost point of the track. Impose a coordinate system with units in meters, the center of the track at the origin, and the northernmost point on the positive y-axis. (Round your answers to two decimal places.) (a) Give Marla's coordinates at her starting point. (x, y) =( (b) Give Marla's coordinates when she has been running for 10 seconds. (x, y) =( (c) Give Marla's coordinates when she has been running for 901.3 seconds. (x, y) =(Explanation / Answer
taking origin as the center of track
equation of motion is of the form (x,y)=(rcos(B(t+c)),-rsin(B(t+c)))
period of one cycle = 58 seconds
2/B =58
=>B=/29
distance covered in 1 cycle = 3 m/s * 58 s =174 m
2 r =174
=>r =(87/)
equation of motion,(x,y)=((87/)cos((/29)(t+c)),-(87/)sin((/29)(t+c)))
initial point is ((87/)cos((/29)(c)),-(87/)sin((/29)(c)))
after 12 seconds point is (0,(87/))
((87/)cos((/29)(12+c)),-(87/)sin((/29)(12+c))) =(0,(87/))
=>(87/)cos((/29)(12+c))=0
=>cos((/29)(12+c))=0
=>((/29)(12+c))=(3/2)
=>(12+c)=(87/2)
=>c=(63/2)
equation of motion,(x,y)=((87/)cos((/29)(t+(63/2))),-(87/)sin((/29)(t+(63/2))))
(a)
for starting point t=0
(x,y)=((87/)cos((/29)(0+(63/2))),-(87/)sin((/29)(0+(63/2))))
(x,y)=((87/)cos(63/58),-(87/)sin(63/58))
(x,y)=(-26.68,7.41)
(b)
after 10 seconds
(x,y)=((87/)cos((/29)(10+(63/2))),-(87/)sin((/29)(10+(63/2))))
(x,y)=(-5.95,27.05)
(c)
after 901.3 seconds
(x,y)=((87/)cos((/29)(901.3+(63/2))),-(87/)sin((/29)(901.3+(63/2))))
(x,y)=(24.03,-13.76)
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