A rider on a bike with the combined mass of 100kgattains aterminal speed of 15m/son a 12% slope. Assuming that the only forces affecting thespeed are the weight and the drag, calculate the drag coefficient. The frontal area is0.9m2.

C_d = 0.942

Explanation:

Let's first calculate the angle of inclination.

Formula is;

tan θ = (%slope)

% Slope is given as 12%

Thus;

θ = tan^(-1) (12/100)

θ = 6.843°

Let's now calculate the force due to the weight of the rider and bike combined from;

F = mg sin θ

We are given; m = 100 kg.

Thus;

F = 100 × 9.81 × sin 6.843

F = 116.885 N

The drag force will also be the same as the force due to the weight of the body. Thus;

Drag force; F = C_d(½ρu²A)

Where;

C_d is drag coefficient

ρ is density

U is terminal speed

A is area

We are given;

A = 0.9 m²

U = 15 m/s

From online tables, density of air is approximately 1.225 kg/m³

Thus;

116.885 = C_d(½ × 1.225 × 15² × 0.9)

116.885 = 124.03125C_d

C_d = 116.885/124.03125

C_d = 0.942

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