Respuesta :
Answer:
The firework will take 5 s to reach the ground again.
Step-by-step explanation:
For the firework to reach the ground it's height must be equal to 0, so we need to solve the given equation for t with h=0. We have:
h = -16t² + 80t
0 = -16t² + 80t
16t² -80t = 0
t(16t - 80) = 0
In this case we have an incomplete second order equation, there are only two values that can satisfy that equality, these are given bellow:
t = 0 s
16t - 80 = 0
16t = 80
t = 80/16 = 5 s
Since 0 s is when it was launched, then 5 s is the time it takes to reach the ground again.
Following are the solution to the given question:
- It appears that [tex]\bold{h(t) = -16t^2+80t + 0}[/tex] is inaccurate. It implies we're launching the ball from the height of zero feet.
- This will not appear to be a possibility. [tex]\bold{h(t) = -16t^2+80t + 0}[/tex] (launched from 6ft above the ground) makes far more sense.
- However, let us return to your issue. We're looking for t when [tex]\bold{h(t) =0}[/tex], thus we'll make our function [tex]\bold{-16t^2+80t = 0}.[/tex]
- Because this is a quadratic with such a missing C term, the equation is [tex]\bold{(Ax^2+Bx+C)}[/tex].
We'll factor it out.
[tex]\to \bold{t(-16t+80) = 0}\\\\\to \bold{-16t+80 = 0}\\\\\to \bold{-16t=-80 }\\\\\to \bold{t=\frac{80}{16} }\\\\\to \bold{t=5 }\\\\[/tex]
Therefore, the ball remains just on the ground for a moment, t = 0 (just before you tossed it), so it rises, falls, and hits the ground again 5 seconds later, [tex]\bold{t = 5}[/tex] , that'swhy, the final answer is "5 seconds".
Learn more:
brainly.com/question/67941
