The resistance to motion of a good bicycle on smooth pavement is nearly all due to aerodynamic drag. Assume that the total mass of rider and bike is M = 100 kg. The frontal area measured from a photograph is A = 0.46 m2. Experiments on a hill, where the road grade is 8 percent, show that terminal speed is Vt = 15 m/s. From these data, drag coefficient is estimated as CD = 1.2.
a) Verify this calculation of drag coefficient.
b) Estimate the distance needed for the bike and rider to decelerate from 15 to 10 m/s while coasting after reaching level road.

Solution :

The road gradient is given as = tan θ = 0.08

So, θ = 457 degrees, sin θ = 0.08

a). While moving downhill, the terminal velocity the forward force which acts due to the gravitation = backward force due to drag

Taking the air density, and putting the values we get

Therefore,

This is approximately the same as the value of coefficient of drag given in the question.

Hence verified.

b). Drag force on level road, F =

  Hence, deceleration :

Integrating both the sides, we get

Hence,

Putting the values,

Distance =

              = -122.5 m

Therefore, ignoring the negative sign, we get distance = 122.5 m

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explanation: