Two bicyclists are riding around circular track as shown in Figure. Cyclist 1 ri

Question

Two bicyclists are riding around circular track as shown in Figure. Cyclist 1 rides around the inside of the track where the radius is 200ft, while cyclist 2 rides around the outside of the track where the radius is 210ft. Both start at theta= zero degrees and v= zero ft/sec at t= zero sec. Both accelerate at a constant rate of 2 ft/sec^2 until they reach a speed of 20 ft/sec after which they maintain a constant speed. When the first cyclist reaches B determine the angular velocity of cyclist 2, and theta 2.

Explanation / Answer

distance to travel by B is 628

time:

first get time to reach 20 velocity:

t = 10sec

distance travelled in that timewill be h = 100

remaining distance is covered with constant v so:

528 = 20*t'

t' = 26.4

total time is 36.4

now for cyclist 2:

distance = 659.4

time to reach 20 will be 10 sec,

now in 26.4 sec it will travel:

x = 26.4*20 = 528

total distance travelled in 36.4 sec will be 628

distance remaining = 31.4

now in circle:

theta = 31.4/210 = .14 rad

and angular velocity will be: w= v/r = .095

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