Physics – Fact and Fancy

Projectiles

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A projectile is anything that is shot, thrown, kicked, batted or other wise placed into the air. Examples in the world of sports would be:  baseballs, footballs, basketballs, golf balls, etc.  The primary force acting on the object is the force of gravity, which is always directed straight down towards the center of the earth.  It is called “free fall.”  Many of you have experienced this feeling before, going over a hill too fast or perhaps on a carnival ride.

There is an old story (for lack of a better term, an old wives tale).  A bullet fired horizontally, and one dropped from the same height and at the same time, will strike the ground simultaneously.  As absurd as this sounds, it is actually true. The time of flight is determined by the equation: 

(vertical height in feet) = 16 (time of flight in seconds)2

The time of flight is determined solely by the vertical height.  Since both bullets start at the same height, they will strike the ground at the same time.  For example, a bullet fired from a height of five feet will strike the ground in 0.56 seconds.  A bullet fired from a high powered rifle (3000 ft/sec) will strike the ground at the same time, but will travel horizontally a distance of almost 1700 feet, or about 1/3 of a mile.

The range of a projectile is defined as the horizontal distance it travels before returning to the same level.  The range is determined primarily by the initial speed and the angle of projection. The range is given by a complicated formula involving trigonometric functions.  As you might expect, the maximum range will occur when the angle is 45o.  To prove this, I would have to resort to a branch of science called calculus.  This is a branch of science that was discovered by Isaac Newton while trying to understand earth’s gravity.  The rifle used in the previous example (3000 ft/s) fired at an angle of 45o, would have a range of about 50 miles. 

I used to tell my students at UAM that they could stand on the steps of the UAM Science Center and kill a deer in Pine Bluff, if they could hit it!

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