Fozzie the dog races Fluffy the cat around a circular flower bed with a radius o

Question

Fozzie the dog races Fluffy the cat around a circular flower bed with a radius of 14 feet. Both animals start at the same time from the 3 o'clock position and run counterclockwise. Fozzie runs at a constant speed of 5 feet per second and Fluffy runs at a constant speed of2.2 feet per second. a. How long does it take Fozzie to run a full lap around the flowerbed? seconds Preview b. How long does it take Fluffy to run a full lap around the flowerbed? secondsPreview c. Define a function, r, that gives the number of feet Fozzie has run from the 3 o'clock position in terms of the number of seconds since he started running, t. Preview d. Define a function, w, that gives the number of feet Fluffy has run from the 3 o'clock position in terms of the number of seconds since he started running, t Preview e. Define a function, m, that gives the distance in feet between Fozzie and Fluffy in terms of the nurnber of seconds since they started running, t. Preview f. How long will it take for Fozzie to pass Fluffy (i.e., to be a full lap ahead of Fluffy)? secondsPreview

Explanation / Answer

Circumference =2pi r = 28 pi

a. speed = 5 feet per second

time = distance/speed = 28pi/5 = 17.6seconds

b. speed = 2.2 feet per seconds

time = 28 pi/2.2 =40ec

c.r(t)= 5* time = 5t

d. w(t)= 2.2*t = 2.2t

e.m = r-w = 5t-2.2 t = 2.8t

f. t = 28pi/2.8 = 31.4 seconds

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