Question

question a large explosion causes wood and metal debris to rise vertically into the air with an initial velocity of 96 feet per second. the quadratic function h(t)=96t - 16t^2 gives the height h (in feet) of the debris at time t (in seconds) after the explosion. how many seconds will it take before the debris falls back to the ground? do not include units in your answer. provide your answer below:

Explanation:

Step1: Set height to 0

When the debris falls back to the ground, $h(t)=0$. So we set up the equation $96t - 16t^{2}=0$.

Step2: Factor out common factor

Factor out $16t$ from the left - hand side of the equation: $16t(6 - t)=0$.

Step3: Use zero - product property

According to the 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 represents the time of the explosion (initial time).
Case 2: $6 - t=0$, which gives $t=6$. This is the time when the debris comes back to the ground.

Answer:

6