A French Bombard Cannon located in Pomme-de-Terre Park in Morris, fires a 123.45

Question

A French Bombard Cannon located in Pomme-de-Terre Park in Morris, fires a 123.456 pound- weight 18 inch diameter projectile at an angle of 56 degree from horizontal with muzzle velocity 112.12m/s from a barrel 38.875 inches in length, mid-point 42.18 inches above ground. Neglecting any influence of the atmosphere, what is the maximum altitude of the projectile, in feet? Neglecting any influence of the atmospere, how far from the end of the cannon barrel does the projectile hit the ground, in miles?

Explanation / Answer

Here ,

initial speed of projectile , v = 112.2 m/s

maximum height of prjectile is h

h = v^2/(2 *g) + ho

h = 112.12^2/*(2 * 9.8) + ho

h = 641.367 m + ho

h = 2107 feet

the maximum altitude of projectile is 2107 feet

as the altitude is very high , we can ignore the initial height

Now, for the distance ,

time of flight , t = 2 * v * sin(theta)/g

t = 2 * 112.12 * sin(56)/9.8

t = 19 s

range = 112.12 * cos(56) * 19

range = 1189.3 m

range = 0.739 miles

the projectile will hit ground 0.739 mile away

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