Question

A projectile is fired vertically upward from a height of 200 feet above the ground, with an initial velocity of 900 ft/sec. Recall that projectiles are modeled by the function h(t)=−16t2+v0t+y0. Write a quadratic equation to model the projectile's height h(t) in feet above the ground after t seconds.

Answer 1

The equation that model the projectile's height is
`h(t) = -16.087\cdot t^(2)+900\cdot t +200`

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:

`h(t) = (1)/(2)\cdot g \cdot t^(2)+v_(o)\cdot t + y_(o)`

Where:

`h(t)` - Current height above the ground at instant t, measured in feet.

`y_(o)` - Initial height, measured in feet.

`v_(o)` - Initial velocity, measured in feet per second.

`g` - Gravitational acceleration, measured in feet per square second.

`t` - Time, measured in seconds.

If we know that
`g = -32.174\,(ft)/(s^(2))`,
`v_(o) = 900\,(ft)/(s)` and
`y_(o) = 200\,ft`, the equation that model the projectile's height is

`h(t) = -16.087\cdot t^(2)+900\cdot t +200`