The Physics of Spiderman's Swing

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Can Spiderman land at the blue mark?
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Contributed by: Stelios Kapranidis and Ron Ruszczyk (April 2014)
Open content licensed under CC BY-NC-SA
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The motion of the pendulum of length can be determined by using the principle of conservation of mechanical energy
,
which gives
.
.
The solution of this differential equation gives the time it takes the pendulum to reach a position
. Using the inverse of this function,
, we find the position of the pendulum at time
as
,
.
When the bob is released at time at position
, the projectile motion of the bob is given by the equations
,
,
where the velocity .
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