Hyperloop: Drag

Classical Mechanics Level 3

The Hyperloop is a hypothetical new fast transport system between cities, which works by launching pods that carry people through a very low air pressure tunnel. The drag force on the \(15000~\mbox{kg}\) Hyperloop pod traveling at approximately \(300~\mbox{m/s}\) is \(320~\mbox{N}\). If the drag force follows the usual law of \(F_d=Cv^2\), where \(C\) is a constant and \(v\) is the velocity, then how long would it take in seconds for the Hyperloop pod to slow down to \(150~\mbox{m/s}\)?

Note: it's a pretty long time, which gives you an idea of why the Hyperloop is pretty energy efficient.

Details and assumptions

  • Assume drag is the only force on the Hyperloop pod.

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