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Answer:
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