We appreciate your visit to A toy rocket is launched straight up from the ground with an initial velocity of tex 80 text ft s tex and returns to the. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
To find the maximum height of the toy rocket, we need to analyze the function modeling its height:
The function given is [tex]\( f(t) = -16t^2 + 80t \)[/tex], where [tex]\( t \)[/tex] is the time in seconds after the rocket is launched.
This function is quadratic, and the graph of a quadratic function is a parabola. Because the coefficient of [tex]\( t^2 \)[/tex] is negative (-16), the parabola opens downwards, meaning it has a maximum point (the vertex).
To find the time at which the maximum height occurs, we use the formula for the vertex of a parabola, [tex]\( t = -\frac{b}{2a} \)[/tex], where [tex]\( a \)[/tex] and [tex]\( b \)[/tex] are the coefficients from the quadratic function:
- Here, [tex]\( a = -16 \)[/tex] and [tex]\( b = 80 \)[/tex].
Plug these values into the formula:
[tex]\[
t = -\frac{80}{2 \times -16} = \frac{80}{32} = 2.5
\][/tex]
So, the rocket reaches its maximum height at [tex]\( t = 2.5 \)[/tex] seconds.
Now, to find the maximum height, substitute [tex]\( t = 2.5 \)[/tex] back into the height function:
[tex]\[
f(2.5) = -16(2.5)^2 + 80(2.5)
\][/tex]
Calculate each part:
1. [tex]\( (2.5)^2 = 6.25 \)[/tex]
2. [tex]\( -16 \times 6.25 = -100 \)[/tex]
3. [tex]\( 80 \times 2.5 = 200 \)[/tex]
Adding these together gives:
[tex]\[
-100 + 200 = 100
\][/tex]
Therefore, the maximum height of the rocket is 100 feet.
The function given is [tex]\( f(t) = -16t^2 + 80t \)[/tex], where [tex]\( t \)[/tex] is the time in seconds after the rocket is launched.
This function is quadratic, and the graph of a quadratic function is a parabola. Because the coefficient of [tex]\( t^2 \)[/tex] is negative (-16), the parabola opens downwards, meaning it has a maximum point (the vertex).
To find the time at which the maximum height occurs, we use the formula for the vertex of a parabola, [tex]\( t = -\frac{b}{2a} \)[/tex], where [tex]\( a \)[/tex] and [tex]\( b \)[/tex] are the coefficients from the quadratic function:
- Here, [tex]\( a = -16 \)[/tex] and [tex]\( b = 80 \)[/tex].
Plug these values into the formula:
[tex]\[
t = -\frac{80}{2 \times -16} = \frac{80}{32} = 2.5
\][/tex]
So, the rocket reaches its maximum height at [tex]\( t = 2.5 \)[/tex] seconds.
Now, to find the maximum height, substitute [tex]\( t = 2.5 \)[/tex] back into the height function:
[tex]\[
f(2.5) = -16(2.5)^2 + 80(2.5)
\][/tex]
Calculate each part:
1. [tex]\( (2.5)^2 = 6.25 \)[/tex]
2. [tex]\( -16 \times 6.25 = -100 \)[/tex]
3. [tex]\( 80 \times 2.5 = 200 \)[/tex]
Adding these together gives:
[tex]\[
-100 + 200 = 100
\][/tex]
Therefore, the maximum height of the rocket is 100 feet.
Thanks for taking the time to read A toy rocket is launched straight up from the ground with an initial velocity of tex 80 text ft s tex and returns to the. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
