5. some fireworks are fired vertically into the air from the ground at an initial speed of 80 feet per…
5. some fireworks are fired vertically into the air from the ground at an initial speed of 80 feet per second. the equation for this objects height h at time t seconds after launch is h = -16t² + 80t. how long will it take the fireworks to reach the ground?
Answer
Explanation:
Step1: Set height equal to 0
When the fireworks reach the ground, $h = 0$. So we set the equation $-16t^{2}+80t = 0$.
Step2: Factor out the common factor
Factor out $-16t$ from the left - hand side of the equation: $-16t(t - 5)=0$.
Step3: Use 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 launch. Case 2: $t - 5=0$, which gives $t=5$. This is the time when the fireworks come back to the ground.
Answer:
5 seconds