How does gravity relate to functions, specifically to s(t)= -1/2 gt^2 + vt + h.
Provide a brief history of the projectile and its use in functions.

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  1. projectile with no air friction and constant acceleration down of g

    Vertical problem:
    initial height = Hi
    initial velocity component UPWARD = Vi
    velocity upward = v
    height = y
    acceleration =-g which is about -9.81 m/s^2 on earth
    v = Vi - g t
    y = Hi + Vi t -(1/2)g t^2

    That is all about up and down
    There are no forces horizontal so the initial horizontal speed is forever until the crash.
    call that speed u
    then horizontal distance x = u t
    you fire missile with speed S and angle up A
    Vi = S sin A
    u = S cos A
    the end :)

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  2. gravity provides a force of attraction between masses

    a force acting on a mass causes it to accelerate

    the function [s(t)= -1/2 gt^2 + vt + h] describes the height (s) relative to time (t) of a mass (object) in freefall
    ... g is the gravitational acceleration
    ... v is the initial vertical velocity
    ... h is the initial height

    due to gravity, projectiles follow a parabolic
    ... the horizontal velocity is constant
    ... while the vertical velocity changes due to gravity

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