Answer:
<h2>19.28 mph</h2>
Step-by-step explanation:
<em>"The question is not complete, here is the complete question</em>
<em>A bicycle with 18-in.-diameter wheels has its gears set so that the chain has a 6-in. radius on the front sprocket and 3-in. radius on the rear sprocket. The cyclist pedals at 180 rpm.</em>
<em>Find the linear speed of the bicycle in in/min (correct to at least two decimal places) </em>
<em>How fast is the bike moving in mph (to two decimal places)?"</em>
Step one:
given data
the diameter of wheels= 18 inches
radius of front sprocket=6 inches
radius of rear sprocket= 3 inches
The cyclist pedals at 180 rpm
The chains move at the same speed, hence
the rear sprocket must make 6/3 revolutions for every one revolution made by the front sprocket
when the rider moves the front sprocket through 180 revs/min
the rear sprocket moves through 180 (6/3) = 360 revs/min
the linear speed of the bicycle in inches per minute =
2π * 9 * 360 = about 20360.16 in/min
<u>The speed in mph</u>
=2π * 9 * 360 * 60 minutes in 1 hr /63360 in/ mile
=19.28 mph
