the sprocket assembly for a 28inch bike tire has a 14 inch r

the sprocket assembly for a 28inch bike tire has a 14 inch radius with a 2 inch radius gear in the center. has fast does the rider have to pedal with a 5 inch radius pedal and gear to go 15 mi/h?

Solution

For 2inch radius pedal tire readius is 14 inch

For 5 inch radius pedal tire radius is 14×5÷2=35 inch

Circumference of tire (one rotation)=2×35=70=219.89 inch=219.89×0.0254=5.585 metre

Speed of cycle=15mi/hr=1609.344×15 m/hr=24140.16 m/Hr

No. Of pedal per hour=24140.16/5.585=4322

Pedal per minute=4322÷60=72