We appreciate your visit to A toy rocket is launched from the ground and its height in meters above the ground at any time tex t tex in seconds is. 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 out how long it will take for the toy rocket to reach the ground, we need to determine when its height is 0 meters. The height of the rocket is given by the equation:
[tex]\[ h(t) = -5t^2 + 20t + 15 \][/tex]
This is a quadratic equation in the form of [tex]\( ax^2 + bx + c = 0 \)[/tex], where [tex]\( a = -5 \)[/tex], [tex]\( b = 20 \)[/tex], and [tex]\( c = 15 \)[/tex].
To find the time [tex]\( t \)[/tex] when the rocket reaches the ground, we set [tex]\( h(t) = 0 \)[/tex]:
[tex]\[ -5t^2 + 20t + 15 = 0 \][/tex]
We can solve this quadratic equation using the quadratic formula:
[tex]\[ t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]
Plug in the values of [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex]:
[tex]\[ t = \frac{-20 \pm \sqrt{20^2 - 4 \cdot (-5) \cdot 15}}{2 \cdot (-5)} \][/tex]
[tex]\[ t = \frac{-20 \pm \sqrt{400 + 300}}{-10} \][/tex]
[tex]\[ t = \frac{-20 \pm \sqrt{700}}{-10} \][/tex]
This simplifies to:
[tex]\[ t = \frac{-20 \pm \sqrt{700}}{-10} \][/tex]
The two values of [tex]\( t \)[/tex] are:
[tex]\[ t = \frac{-20 + \sqrt{700}}{-10} \][/tex] and [tex]\[ t = \frac{-20 - \sqrt{700}}{-10} \][/tex]
These calculations yield two solutions:
1. [tex]\( t = 2 - \sqrt{7} \)[/tex]
2. [tex]\( t = 2 + \sqrt{7} \)[/tex]
The time when the rocket hits the ground is a positive value, so we choose the positive solution:
[tex]\[ t = 2 + \sqrt{7} \][/tex]
Thus, the rocket will reach the ground approximately [tex]\( 2 + \sqrt{7} \)[/tex] seconds after it is launched.
[tex]\[ h(t) = -5t^2 + 20t + 15 \][/tex]
This is a quadratic equation in the form of [tex]\( ax^2 + bx + c = 0 \)[/tex], where [tex]\( a = -5 \)[/tex], [tex]\( b = 20 \)[/tex], and [tex]\( c = 15 \)[/tex].
To find the time [tex]\( t \)[/tex] when the rocket reaches the ground, we set [tex]\( h(t) = 0 \)[/tex]:
[tex]\[ -5t^2 + 20t + 15 = 0 \][/tex]
We can solve this quadratic equation using the quadratic formula:
[tex]\[ t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]
Plug in the values of [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex]:
[tex]\[ t = \frac{-20 \pm \sqrt{20^2 - 4 \cdot (-5) \cdot 15}}{2 \cdot (-5)} \][/tex]
[tex]\[ t = \frac{-20 \pm \sqrt{400 + 300}}{-10} \][/tex]
[tex]\[ t = \frac{-20 \pm \sqrt{700}}{-10} \][/tex]
This simplifies to:
[tex]\[ t = \frac{-20 \pm \sqrt{700}}{-10} \][/tex]
The two values of [tex]\( t \)[/tex] are:
[tex]\[ t = \frac{-20 + \sqrt{700}}{-10} \][/tex] and [tex]\[ t = \frac{-20 - \sqrt{700}}{-10} \][/tex]
These calculations yield two solutions:
1. [tex]\( t = 2 - \sqrt{7} \)[/tex]
2. [tex]\( t = 2 + \sqrt{7} \)[/tex]
The time when the rocket hits the ground is a positive value, so we choose the positive solution:
[tex]\[ t = 2 + \sqrt{7} \][/tex]
Thus, the rocket will reach the ground approximately [tex]\( 2 + \sqrt{7} \)[/tex] seconds after it is launched.
Thanks for taking the time to read A toy rocket is launched from the ground and its height in meters above the ground at any time tex t tex in seconds is. 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
