Constructed Response Task
An object is launched at 144 feet per minute (ft/m) from a 576 feet tall tower. The equation for
the object's heights at timer minutes after launch is
s(t) = -1672 +1441 +576, where s is in feet. When does the object land on the ground
and why?

The object takes 12 minutes to land on the ground.

Explanation:

Given that the equation for the object's height s at time t minutes after the launch is

We need to determine the time that it takes for the object to land on the ground.

Time taken:

The time t of an object can be determined by substituting

Thus, we have,

Switch sides,

Thus, we get,

Let us solve the equation using the quadratic formula.

Thus, the values of t are and

Simplifying, we get,

and

 and

Since, the value of t cannot be negative, then

Thus, the object takes 12 minutes to land on the ground.