Question

(4 pts) Imagine that there is a circular track given by the equation x2+y2=2102500, where both x and y are measured in units of feet. At time t=0, Robin is at point (1450,0) and Shannon is at point (−170,1440). Both are running counterclockwise, with Shannon running at 2.3 feet per second and Robin running at 3.6 feet per second.

Robin runs until he catches Shannon. How long does that take (in seconds)?


At what point do Robin and Shannon meet?

Answer 1

radius of circle = 1450 ft

circumference of whole track = 2π(1450)
= 2900π ft

angle of sector between them
= 90 + arctan(1440/170) = 173.267°

Distance Robin has to make up is

173.267/360 = x/2900π
x = 4384.9155 ft


He is gaining on him at a rate of
1.3 ft/sec
so to catch up on the 4384.9155 ft would take

4384.9155/1.3 seconds
= 3373.01 seconds

unreasonable answer?
no, unreasonable question.