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A model rocket is launched from ground level. Its height, h meters above the ground, is a function of time t seconds after launch and is given by the equation . What would be the maximum height, to the nearest meter, attained by the model? (First find the axis of symmetry x= (-b/2a), then plug this value into the equation)

Answer :

Answer:

The maximum height attained by the rocket is 240.1 m.

Step-by-step explanation:

The height above the ground is a function of time t is given by :

[tex]h= -4.9t^2 + 68.6t[/tex] ...(1)

We need to find the maximum height of the model. First we find the time of max height using axis of symmetry of the equation as follows :

[tex]x=\dfrac{-b}{2a}[/tex]

We have, a = -4.9 and b = 68.6

So,

[tex]t=\dfrac{-(68.6)}{2\times -4.9}\\\\=7\ s[/tex]

Put t = 7 in equation (1)

[tex]h= -4.9(7)^2 + 68.6(7)\\\\=240.1\ m[/tex]

So, the maximum height attained by the rocket is 240.1 m.

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