Suppose the wheels on the mountain bike have a radius of 33 centimeters. a) How far does the bike travel for each complete revolution of the 14 tooth rear sprocket? b) How far does the bike travel for each complete revolution of the front pedal sprocket? c) If the rider pedal is at an angular velocity of 80 rpm, how far will she travel in one minute? d) How long will the rider need to pedal at 80 rpm to travel 2 kilometers?

a) 207.34 cm

b) 622 cm

c) 497.60 m/min

d) 4.02 min

Step-by-step explanation:

Radius of bike = 33 cm

Rear sprocket = 14 teeth

Pedal sprocket = 42 teeth (missing information in the question)

Transmission gear ratio = 42/14 = 3

a) How far does the bike travel for each complete revolution of the 14 tooth rear sprocket?

Distance traveled with rear wheel is

D = 2*π*r = 2*π*33 = 207.34 cm

b) How far does the bike travel for each complete revolution of the front pedal sprocket?

Distance traveled with front pedal is

D = Transmission gear ratio * Distance traveled with rear wheel

D = 3*207.34 = 622 cm

c) If the rider pedal is at an angular velocity of 80 rpm, how far will she travel in one minute?

D = 80*622 = 49760 cm or 497.60 meters per min

Therefore, the rider will travel 497.60 m/min at an angular velocity of 80 rpm.

d) How long will the rider need to pedal at 80 rpm to travel 2 kilometers?

t = Distance/rate

t = 2000/497.60 = 4.02 min

Therefore, it will take the rider 4.02 mins to pedal at 80 rpm to travel 2 km.