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Prj21 Cannon fired from bluff

Transported back in time you are in charge of harbor defenses for a coastal city. Using the recently developed length standard, the meter, (Paris Academy of Science, 1791) you determine that a bluff 50 meters over a narrow channel (the only approach to the city from the sea) is 180 meter from the narrow channel. From past experiments you know the relationship between amount of powder and muzzle velocity for your cannon.

Mounting the cannon so they fire horizontally, what initial velocity is required to fire cannon balls into the channel at the 180 meter distance?

Diagram the problem and add the coordinate system.

Write the six equations for the motion of the cannon ball.

Look over the six equations and decide how to proceed. Remember that the y-velocity is the initial velocity and this stays constant throughout the motion. There is no acceleration in the y-direction.

The desired x and y are known so set x = 50 m and solve for the time of flight.

With the time of flight and the required range the initial velocity, v_o, can be calculated.

Notice in this problem that the axes are choosen for convenience in doing the problem. Making x positive down and y positive to the right makes for simpler equations than for the x positive to the right and y positive up orientation.