2. Gretchken has made a circular running track in the middle of the farm. The tr

Question

2. Gretchken has made a circular running track in the middle of the farm. The track has an inner radius of 15 meters, and a thickness of 3 meters and is depicted below. When Chuck and Samsa fail to return, Gretchken starts running to alleviate her anxiety. 3 m 15 m starting position center of track (a) First, Gretchken runs counterclockwise following the outside edge of the track at a constant speed of 1.2 meters/second for 10 minutes. What is the total angular distance (in radians) that she covers in 10 minutes? (b) After 10 minutes, she stops, and moves to the inner edge of the track, taking a 2 minute break in total. She then continues running counterclockwise following the inner edge of the track at the same constant speed for another 8 minutes. What is the total angular distance (in radians) that she covers in these 8 minutes? c) Write a formula for a piecewise function A(t) giving the total angular distance (in radians) that she has run t minutes after she first started running (be sure to take into account her 2 minute break!). (d) Suppose Gretchen's run (as described in parts (a) and (b)) began at the point labeled "starting position on the figure. Draw a diagram that shows her position on the track when she stops running. Label her angle in radians relative to the dotted line in the diagram. Please leave your answers in exact form.

Explanation / Answer

a) solution: Outer radius=15+3 =18.

We know that the angular distance =v/r

=1.2/18 =0.0666..

Thus angular distance in 10 minutes = 10*60*0.666

= 40 radian.

b) Inner radius =15 m.

thus angular distance cover in 8 min. =1.2 *8*60/15=38.4 radian.

c) Function for angular distance A(t)

=1.2*t*60/18+ 1.2*(t-2)*60/15

=4t+4.8(t-2)

Related Questions

Navigate

• Browse (All)
• Browse 2
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.