Question

An 80 kg cyclist is riding her 13 kg bike downhill on a road with a slope of 11⁰ without pedalling or braking. she has a frontal area of 0.45 m² and a drag coefficient of 1.1 when upright, and a frontal area of 0.42 m² and a drag coefficient of 0.9 if she gets into "the racing position", leaning down over the handlebars. ignore rolling resistance of the tyres and other friction in the system. (assume the density of air to be 1.25kg/m³)

Determine the terminal velocity of the cyclist if she is in the upright position. km/hr

Answer 1

To determine the terminal velocity of the cyclist in the upright position, we use the formula for drag force and solve for velocity. Substituting the given values, we can calculate the terminal velocity in m/s and then convert it to km/hr.

Step-by-step explanation:

To determine the terminal velocity of the cyclist in the upright position, we need to calculate the drag force acting on the cyclist. The drag force can be calculated using the formula:

Drag Force = 0.5 * Drag Coefficient * Air Density * Frontal Area * Velocity^2

Solving for velocity, we can rearrange the formula:

Velocity = sqrt((2 * Weight) / (Drag Coefficient * Air Density * Frontal Area))

Substituting the given values, we have:

Velocity = sqrt((2 * 80 * 9.8) / (1.1 * 1.25 * 0.45))

Calculating this value will give us the terminal velocity in m/s. To convert it to km/hr, we can use the conversion factor: 1 m/s = 3.6 km/hr.