Question

Constructed Response Task

Answer 1

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 $s(t)=-16t^2+144t+576$

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 $s(t)=0$

Thus, we have,

$0=-16t^2+144t+576$

Switch sides,

Thus, we get,

$-16 t^{2}+144 t+576=0$

Let us solve the equation using the quadratic formula.

$t=\frac{-144 \pm \sqrt{144^{2}-4(-16) 576}}{2(-16)}$

$t=\frac{-144 \pm \sqrt{20736+36824}}{-32}$

$t=\frac{-144 \pm \sqrt{57600}}{-32}$

$t=\frac{-144 \pm 240}{-32}$

Thus, the values of t are $t=\frac{-144 + 240}{-32}$ and $t=\frac{-144 -240}{-32}$

Simplifying, we get,

$t=\frac{96}{-32}$ and $t=\frac{-384}{-32}$

$t=-3$  and $t=12$

Since, the value of t cannot be negative, then $t=12$

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