Use bisection to determine the drag coefficient needed so that a 65kg bungee jumper has a velocity of 35m/s after 4.5s of free f
all. Note: The acceleration of gravity is 9.81m/s2. Start with initial guesses of xl= 0.2 and xu= 0.3 and iterate until the approximate relative error falls below 2%.
1 answer:
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Answer:
0·95
Explanation:
Given the combined mass of the rider and the bike = 100 kg
Percent slope = 12%
∴ Slope = 0·12
Terminal speed = 15 m/s
Frontal area = 0·9 m²
Let the slope angle be β
tanβ = 0·12
As it attains the terminal speed, the forces acting on the combined rider and the bike must be balanced and therefore the rider must be moving download as the directions of one of the component of weight and drag force will be in opposite directions
The other component of weight will get balance by the normal reaction and you can see the figure which is in the file attached
From the diagram m × g × sinβ = drag force
Drag force = 0·5 × d × × v² × A
where d is the density of the fluid through which it flows
is the drag coefficient
v is the speed of the object relative to the fluid
A is the cross sectional area
As tanβ = 0·12
∴ sinβ = 0·119
Let the fluid in this case be air and density of air d = 1·21 kg/m³
m × g × sinβ = 0·5 × d × × v² × A
100 × 9·8 ×0·119 = 0·5 × 1·21 × × 15² × 0·9
∴ ≈ 0·95
∴ Drag coefficient is approximately 0·95
