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If a toy rocket is launched vertically upward from the ground with an initial velocity of 128 feet per second, then its height after [tex]t[/tex] seconds is given by the equation [tex]h(t)[/tex].

Answer :

If a toy rocket is launched vertically upward from the ground with an initial velocity of 128 feet per second, the object will reach its maximum height after 4 seconds. The correct option is D.

To estimate the maximum height attained by the toy rocket, we must first determine when the vertical velocity reaches zero.

The height is a quadratic function of time in the equation h(t) = -[tex]16t^2[/tex] + 128t. The greatest height is attained at the parabolic curve's vertex.

The vertex of a quadratic function in the form h(t) = at^2 + bt + c can be found using the formula t = -b / (2a).

In this case, a = -16 and b = 128. Plugging these values into the formula:

t = -128 / (2(-16))

t = -128 / (-32)

t = 4

Thus, the object will reach its maximum height after 4 seconds. The correct option is D.

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Your question seems incomplete, the probable complete question is:

If a toy rocket is launched vertically upward from ground level with an initial velocity of 128 feet per second then its height H after T seconds is given by the equation h(t)=-16t^2+128t (if air resistance is neglected). When will the object reach its maximum height?

A. 8 seconds

B. 6 seconds

C. 0 seconds

D. 4 seconds​

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