Respuesta :
Answer:
The equation for the height, in ft, is:
[tex]h(t)=-16.085\cdot t^2+64\cdot t[/tex]
Step-by-step explanation:
The height can be expressed as an integration of the speed:
[tex]h(t)-h(0)=h(t)=\int_{0}^t v(t)\,dt[/tex]
Also, the speed can be expressed as an integration of the acceleration:
[tex]v(t)-v(0)=v(t)-64=\int_0^ta(t)\,dt=-g\cdot t=-32.17t\\\\v(t)=64-32.17t \;[ft/s][/tex]
Then, if we go to the height equation, we have:
[tex]h(t)=\int_{0}^t v(t)\,dt=64t-32.17\cdot \dfrac{t^2}{2}=64t-16.085t^2[/tex]
The equation for the height is:
[tex]h(t)=-16.085\cdot t^2+64\cdot t[/tex]
The required quadratic function is [tex]h=64t-16.085t^2[/tex]
Quadratic Function:
A quadratic function is a polynomial of degree 2 and so the equation of quadratic function is of the form [tex]f (x) = ax^ 2 + bx + c[/tex]
Given that,
Initial velocity of Rocket, u = 64 feet/sec.
Considering acceleration due to gravity [tex]32.17 \ feet/sec^2[/tex]
Height of the rocket can be given as,
[tex]h=ut-\frac{1}{2}\times 32.17\times t^2\\ h=64t-16.085t^2\\[/tex]
Learn more about the topic Quadratic Function:
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