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*Question:* A cannon placed on a 50m high cliff
fires a cannonball over the edge of the cliff at
making an angle
of
to the horizontal. How long is the cannonball in the air? Neglect
air resistance.

*Answer:* In order to answer this question we need only consider the cannonball's
vertical motion. At (*i.e.*, the time of firing) the cannonball's height off the
ground is m and its velocity component in the vertical direction is
. Moreover,
the cannonball is accelerating vertically downwards at
.
The equation of vertical motion of the cannonball is written

where is the cannonball's height off the ground at time . The time of flight
of the cannonball corresponds to the time at which . In other words,
the time of flight is the solution of the quadratic equation

Hence,

Here, we have neglected the unphysical negative root of our quadratic equation.

** Next:** Worked example 3.4: Hail
** Up:** Motion in 3 dimensions
** Previous:** Worked example 3.2: Gallileo's
Richard Fitzpatrick
2006-02-02