Hold on, Indy!

Classical Mechanics Level 3

A standard action movie scene is the following: the hero or heroine is on a bridge when the most devious evil bad guys cut the supports on one side of the bridge, leaving the hero/heroine to cling desperately to the bridge as it slowly swings down. Then there's the camera shot over the side of the cliff as we wait to see if the hero or heroine actually held on to the bridge and is now climbing back up.

Our \(70~\mbox{kg}\) heroine is two-thirds of the way across a horizontal \(30~\mbox{m}\) long bridge over a canyon with perfectly vertical walls. The bad guys then cut the supports of the bridge (she is closer to where the supports are cut than the other side). The bridge, which can be modeled as a rod of mass \(500~\mbox{kg}\) and uniform density, then begins to rotate downwards with our heroine clinging to it. How fast is the heroine traveling in m/s when she hits the canyon wall?

Details and assumptions

  • The acceleration of gravity is \(-9.8~\mbox{m/s}^2\).
  • Treat the heroine as a point mass.
  • Neglect air resistance.

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