Answered

The radii of the sprocket assemblies and the wheel of the bicycle in the figure are:

4 inches,

2 inches,

and 14 inches respectively.


If the cyclist is pedaling at a rate of 1 revolution per second, find the speed of the bicycle in (a) feet per second and (b) miles per hour.

Verified Answer :

antonsandiego

To solve this task we have to make a proportion, but firstly we have to set up all the main points : so, the distance is  s=r(B), that has its r=radius,B=angle in rad
velocity v=ds/dt= w(r)
Do not forget about  w = angular speed in rad/s and \(w1 = 1 revolution/sec = 2Pi (rad/s)\)
Now we can go to proportion
\(v1=v2\)
\(w1*r1 = w2r2\)\(w2 = w1 * r1/r2 = 2w1 = 4Pi (rad/s)\)
\(w2 = w3 (which is the angular velocity of the rear wheel)\)
SOLVING FOR A : \(v3 = w3 * r3 = 4pi * 14 (inch/s) = 14.66 ft/sec\)
\(v3 = 14.66 ft/sec(1 mile/5280 ft)( 3600 sec/h)\)\(= 9.99\) or something about 10 mph --- SOLVING FOR B.
I'm sure it helps!

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