an object is launched from the ground. the objects height, in feet, can be described by the quadratic…

an object is launched from the ground. the objects height, in feet, can be described by the quadratic function $h(t)=80t - 16t^{2}$, where $t$ is the time, in seconds, since the object was launched. when will the object hit the ground after it is launched? explain how you found your answer.

an object is launched from the ground. the objects height, in feet, can be described by the quadratic function $h(t)=80t - 16t^{2}$, where $t$ is the time, in seconds, since the object was launched. when will the object hit the ground after it is launched? explain how you found your answer.

Answer

Explanation:

Step1: Set height equal to 0

When the object hits the ground, $h(t)=0$. So we set up the equation $80t - 16t^{2}=0$.

Step2: Factor out common factor

Factor out $16t$ from the left - hand side of the equation: $16t(5 - t)=0$.

Step3: Use zero - product property

If $ab = 0$, then either $a = 0$ or $b = 0$. So we have two cases: Case 1: $16t=0$, which gives $t = 0$. This is the time of launch. Case 2: $5 - t=0$, which gives $t = 5$. This is the time when the object hits the ground after being launched.

Answer:

5 seconds