Answer:
The equation that model the projectile's height is [tex]h(t) = -16.087\cdot t^{2}+900\cdot t +200[/tex]
Step-by-step explanation:
We know that projectile is fired vertically upward from a height of 200 feet above the ground with an initial velocity of 900 feet per second and projectiles experiment a parabolic motion, which combines horizontal uniform motion and vertical uniform accelerated motion due to gravity, whose equation of motion is:
[tex]h(t) = \frac{1}{2}\cdot g \cdot t^{2}+v_{o}\cdot t + y_{o}[/tex]
Where:
[tex]h(t)[/tex] - Current height above the ground at instant t, measured in feet.
[tex]y_{o}[/tex] - Initial height, measured in feet.
[tex]v_{o}[/tex] - Initial velocity, measured in feet per second.
[tex]g[/tex] - Gravitational acceleration, measured in feet per square second.
[tex]t[/tex] - Time, measured in seconds.
If we know that [tex]g = -32.174\,\frac{ft}{s^{2}}[/tex], [tex]v_{o} = 900\,\frac{ft}{s}[/tex] and [tex]y_{o} = 200\,ft[/tex], the equation that model the projectile's height is
[tex]h(t) = -16.087\cdot t^{2}+900\cdot t +200[/tex]
