Leap Of Faith

Hello everyone, I was viewing the TV commercial of the Audi TT Advert. Just thought I would make a problem based on this. Please watch the video first before reading further. Here is the video link.

Suppose the car started its descent from the edge of the atmosphere where the gravitational acceleration does not vary that much. Because of the atmosphere assume that the drag force is \(bv\) where \(b\) is a dimensionless coefficient and \(v\) is the velocity of the car at a particular instant. Find the distance travelled by the car as a function of distance \(x(t)\). Also, find the power given off by the frictional forces of the drag once it achieves terminal velocity. I will soon include a sound version for this problem because of the much speeds involved.(\(V_{\text{terminal}}=\dfrac{mg}b \)).

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