We appreciate your visit to A projectile with an initial velocity of 48 feet per second is launched from a building 190 feet tall What is the maximum height of. 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 determine the maximum height reached by the projectile, you can use the information provided by the quadratic equation that models its path:
[tex]\[ h(t) = -16t^2 + 48t + 190 \][/tex]
This equation represents a parabola, where [tex]\( h(t) \)[/tex] is the height of the projectile at time [tex]\( t \)[/tex]. To find the maximum height, we need to find the vertex of the parabola because the vertex represents the highest point for a downward-opening parabola like this one.
1. Identify the coefficients: The equation [tex]\( h(t) = -16t^2 + 48t + 190 \)[/tex] is in the standard quadratic form [tex]\( ax^2 + bx + c \)[/tex]. Here, [tex]\( a = -16 \)[/tex], [tex]\( b = 48 \)[/tex], and [tex]\( c = 190 \)[/tex].
2. Find the time at which the maximum height occurs: The formula to find the time [tex]\( t \)[/tex] at which the vertex (maximum height) occurs is given by:
[tex]\[ t = -\frac{b}{2a} \][/tex]
Plug the values into the formula:
[tex]\[ t = -\frac{48}{2 \times -16} \][/tex]
[tex]\[ t = -\frac{48}{-32} \][/tex]
[tex]\[ t = 1.5 \][/tex]
So, the projectile reaches its maximum height at 1.5 seconds.
3. Calculate the maximum height: Substitute [tex]\( t = 1.5 \)[/tex] back into the original equation to find the maximum height:
[tex]\[ h(1.5) = -16(1.5)^2 + 48(1.5) + 190 \][/tex]
[tex]\[ h(1.5) = -16(2.25) + 72 + 190 \][/tex]
[tex]\[ h(1.5) = -36 + 72 + 190 \][/tex]
[tex]\[ h(1.5) = 226 \][/tex]
Therefore, the maximum height reached by the projectile is 226 feet.
[tex]\[ h(t) = -16t^2 + 48t + 190 \][/tex]
This equation represents a parabola, where [tex]\( h(t) \)[/tex] is the height of the projectile at time [tex]\( t \)[/tex]. To find the maximum height, we need to find the vertex of the parabola because the vertex represents the highest point for a downward-opening parabola like this one.
1. Identify the coefficients: The equation [tex]\( h(t) = -16t^2 + 48t + 190 \)[/tex] is in the standard quadratic form [tex]\( ax^2 + bx + c \)[/tex]. Here, [tex]\( a = -16 \)[/tex], [tex]\( b = 48 \)[/tex], and [tex]\( c = 190 \)[/tex].
2. Find the time at which the maximum height occurs: The formula to find the time [tex]\( t \)[/tex] at which the vertex (maximum height) occurs is given by:
[tex]\[ t = -\frac{b}{2a} \][/tex]
Plug the values into the formula:
[tex]\[ t = -\frac{48}{2 \times -16} \][/tex]
[tex]\[ t = -\frac{48}{-32} \][/tex]
[tex]\[ t = 1.5 \][/tex]
So, the projectile reaches its maximum height at 1.5 seconds.
3. Calculate the maximum height: Substitute [tex]\( t = 1.5 \)[/tex] back into the original equation to find the maximum height:
[tex]\[ h(1.5) = -16(1.5)^2 + 48(1.5) + 190 \][/tex]
[tex]\[ h(1.5) = -16(2.25) + 72 + 190 \][/tex]
[tex]\[ h(1.5) = -36 + 72 + 190 \][/tex]
[tex]\[ h(1.5) = 226 \][/tex]
Therefore, the maximum height reached by the projectile is 226 feet.
Thanks for taking the time to read A projectile with an initial velocity of 48 feet per second is launched from a building 190 feet tall What is the maximum height of. 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
