Question

A bicycle pedals at such a rate that both wheels rotate at 235. rpm. the outside wheel diameter is 26.0in . Assuming that the tires never slip against the ground, what is the bicyclist's speed in mph?​

A) 8.63 mph
B) 17.26 mph
C) 21.58 mph
D) 34.52 mph

Answer 1

The bicyclist's speed, given a wheel rotation of 235 rpm and a wheel diameter of 26.0 inches, is calculated using circumference and conversion factors, resulting in a speed of 17.26 mph.

Step-by-step explanation:

The question is asking for the speed of a bicyclist in miles per hour (mph) given that both wheels of the bicycle rotate at 235 revolutions per minute (rpm) and that the bicycle wheel diameter is 26.0 inches. To solve this, we need to convert the angular speed (rpm) into linear speed. Here is the step-by-step process:

1. Convert rpm to revolutions per second (fps) by dividing 235 rpm by 60 seconds per minute.
2. Calculate the circumference of the wheel using the formula: circumference = π * diameter.
3. Find the distance traveled per second by multiplying the rps by the circumference of the wheel.
4. Convert this distance per second to miles per hour by appropriate conversions (1 inch = 0.0254 meters, 1 meter = 0.000621371 miles, and 3600 seconds = 1 hour).

By putting these calculations together, we can find that the bicyclist's speed in mph. Applying the above process, we find that the correct answer is 17.26 mph (Option B).