An object is propelled upward from the top of a 300 foot building. the path that the object takes as it falls to the ground can be modeled by h = 16t^2 + 80t + 300 where t is the time (in seconds) and h is the corresponding height (in feet) of the object. how long does it take the object to hit the ground?

As per the statement:

The path that the object takes as it falls to the ground can be modeled by  

h =-16t^2 + 80t + 300

where

h is the height of the objects and

t is the time (in seconds)

At t = 0 , h = 300 ft

When the objects hit the ground, h = 0

then;

-16t^2+80t+300=0

For a quadratic equation: ax^2+bx+c=0         ......[1]

the solution for the equation is given by:

On comparing the given equation with [1] we have;  

a = -16 ,b = 80 and c = 300

then;

Simplify:

= -2.5 sec and = 7.5 sec

Time can't be in negative;

therefore, the time it took the object to hit the ground is 7.5 sec

It takes 7.5 seconds the object to hit the ground.

Step-by-step explanation:

An object is propelled upward from the top of a 300 foot building. The path that the object takes as it falls to the ground can be modeled by:

h = -16t^2 + 80t + 300

where:

t is the time (in seconds) and

h is the corresponding height (in feet) of the object.

How long does it take the object to hit the ground?

When the objet hit the ground:

h=0

Then, equaling h (the equation) to zero:

This is a quadratic equation. Using the quadratic formula:

Two solutions:

The first solution is not possible, because the time can't be a negative number, then the solution is the second one: t=7.5 seconds

It takes 7.5 seconds the object to hit the ground.