Question

After t seconds, the height h(t) of a model rocket launched from the ground into the air is given by the function h(t)=-16t^2+80t. Find how long it takes the rocket to reach a height of 96 feet

Answer 1

Lol, why does this sound like one of my seventh grade algebra teacher's problem. Anyway, back to the problem...

The reason why you don't understand this problem is probably because you don't clearly understand h(t) and t itself, and its meaning in the context.

h(t) shows the actual distance from the ground.

t is the actual time after the launch.

For example, when t = 1, it's one second into the launch. Using the function of h(t) = -16t^2 + 80t, we can find the distance off the ground. Doesn't make sense? Feel free to ask questions in the comments below.

So, the question is asking how long it takes the rocket to reach a height of 96 feet. We are trying to find the TIME, which is known as "t," right?

So, what should we do with the "96"? We should plug this in...

96 = -16t^2 + 80t

What we're doing here is showing that some time after the launch, it got up to 96 feet, and we are representing it with this function and plugging in 96 as h(t). At this point, all we have to do is solve the quadratic.

-16t^2 + 80t = 96

-16t^2 + 80t - 96 = 0

WE HAVE TO NOW SIMPLIFY.

-8t^2 + 40t - 48 = 0

-4t^2 + 20t - 24 = 0

-2t^2 + 10t - 12 = 0

-t^2 + 5t - 6 = 0

t^2 - 5t + 6 = 0

(Sorry i did so many steps i'm so tired and my brain is just garbonzo bean fried)

t^2 - 5t + 6 = 0

TWO NUMBERS WHICH MULTIPLY TO 6 AND ADD TO -5

-3 and -2

yaaaaaaaaaaaay

t^2 - 3t - 2t + 6 = 0

t ( t - 3) - 2 ( t - 3 ) = 0

(t - 2) (t - 3) = 0

t = 2, t = 3

So basically, it takes t = 2 because the two answers means that it got up to 96 ft in two seconds and then it was going down at 3 seconds and reached 96 ft. Make sense? Just feel free to ask me anything and give me brainliest lol

***credits to my fabulous 7th grade math teacher, Ms. Lam, for teaching me all of this