Projectile motion

A projectile near the surface of the earth has two independent motions: A horizontal motion at constant speed and a vertical motion subject to the acceleration due to gravity.

In order to deal with any problem in projectile motion, one has to choose a coordinate system and also to clearly specify the origin. If the x axis is horizontal and the у axis points vertically upward, then

a_x = 0; a_y=-g

One can usually pick the origin such that the initial horizontal (x) coordinate is zero, that is, x₀ = 0. The equations of kinematics for projectiles near the earth's surface take the form:

(2.13)

(2.14)

(2.15)

It is essential that you maintain the x and у subscripts in these equations. Notice in particular that it is the vertical component, υ _0y, of the initial velocity, rather than υ ₀ itself, that appears in the last two equations.

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