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## Worked example 3.3: Cannon shot

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