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Today’s Problem: Fallturm Bremen drop tower initial velocity
What is the initial velocity of a projectile shot straight up the 122 meter drop tube at Fallturm Bremen that reaches the height of the tube before beginning its descent?
At the top end of the tube, the initial kinetic energy of the projectile becomes all gravitational potential energy:
\[\mathrm{KE} = \mathrm{PE}\] \[\frac{1}{2}mv^2 = mgh\] where
- \(m=\) mass of the projectile
- \(v=\) initial velocity of the projectile
- \(g=\) acceleration due to gravity \(= 9.8\) m/s\(^2\)
- \(h=\) height the projectile reaches \(= 122\) m
Cancelling the mass on both sides and solving for \(v\) gives:
\[\begin{eqnarray}v &=& \sqrt{2gh}\nonumber\\ &=& \sqrt{2(9.8\mathrm{m/s}^2)(122\mathrm{m})}\nonumber\\ &=& 49\;\mathrm{m/s} = 176\;\mathrm{km/hr} = 110\;\mathrm{mi/hr}\nonumber \end{eqnarray}\] Note that this initial velocity is independent of the mass of the projectile.
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