Queenangie2
contestada

raven built a rocket for her science project and launched it from a platform to track its path. the hight in feet of the rocket above ground at time t seconds can be modeled by the equation h= -16t^2+32t+4 what is the maximum hight the rocket reaches

Respuesta :

Answer:

20ft

Step-by-step explanation:

-16t² + 32t + 4

The main goal to find the maximum height is to find the vertex of the parabola because the vertex is always the minimum or the maximum value.

To find the x value of the vertex, use the formula x = [tex]\frac{-b}{2a}[/tex]

The a-value is the first coefficient and the b value is the second coefficient:

x = [tex]\frac{-32}{-32}[/tex]

x = 1

We can say x = t because t is the x value in the equation.

Now, we can substitute x back into the original equation to find the y-value for the vertex.

y = -16t² + 32t + 4

y = -16(1)² + 32(1) + 4

y = -16(1) + 32 + 4

y = -16 + 32 + 4

y = 20

In a word problem, height is typically the y-value and time is typically the x-value. Since t = x, the answer is 20.

abidemiokin

The maximum height the rocket reaches is 20ft/s

Given the equation of the height reached by the rocket expressed according to the equation as;

[tex]h= -16t^2+32t+4[/tex]

At the maximum, the velocity of the rocket is zero i.e. [tex]\frac{dh}{dt} = 0[/tex]

Differentiating the function to get the velocity function;

[tex]v(t) = -32t + 32\\0 = -32t + 32\\32t = 32\\t = \frac{32}{32}\\t = 1 sec[/tex]

Get the maximum height the rocket reaches

[tex]h(1)= -16(1)^2+32(1)+4\\h(1) =-16 + 32 + 4\\h(1)=20ft/s[/tex]

Hence the maximum height the rocket reaches is 20ft/s

Learn more on velocity functions here;https://brainly.com/question/25749514

Otras preguntas