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Answer :
The height of the rocket is modeled by the function:
[tex]f(t)=-16 t^{2}+80t [/tex]
If we observe this equation, we see that the function is quadratic. The shape of the quadratic function is parabolic and the maximum or minimum value of a parabola always lies at its vertex. In the given function, since the co-efficient of leading term (t²) is negative, so this parabola will have a maximum value at its vertex.
The vertex of parabola is given by:
[tex]( \frac{-b}{2a}, f( \frac{-b}{2a})) [/tex]
b is the coefficient of t term. So b = 80
a is the coefficient of squared term. So a= - 16
So,
[tex] \frac{-b}{2a}= \frac{-80}{2(-16)}= \frac{5}{2}=2.5 [/tex]
This means at 2.5 sec the height of rocket will be maximum. The maximum height will be:
[tex]f(2.5)=-16 (2.5)^{2}+80(2.5)=100 [/tex]
Therefore, the maximum height of the rocket will be 100 feet.
[tex]f(t)=-16 t^{2}+80t [/tex]
If we observe this equation, we see that the function is quadratic. The shape of the quadratic function is parabolic and the maximum or minimum value of a parabola always lies at its vertex. In the given function, since the co-efficient of leading term (t²) is negative, so this parabola will have a maximum value at its vertex.
The vertex of parabola is given by:
[tex]( \frac{-b}{2a}, f( \frac{-b}{2a})) [/tex]
b is the coefficient of t term. So b = 80
a is the coefficient of squared term. So a= - 16
So,
[tex] \frac{-b}{2a}= \frac{-80}{2(-16)}= \frac{5}{2}=2.5 [/tex]
This means at 2.5 sec the height of rocket will be maximum. The maximum height will be:
[tex]f(2.5)=-16 (2.5)^{2}+80(2.5)=100 [/tex]
Therefore, the maximum height of the rocket will be 100 feet.
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