A rocket is propelled upward from the top of a building 220 feet tall at an initial velocity of 112 feet...

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29. A rocket is propelled upward from the top of a building 220 feet tall at an initial velocity of 112 feet per second. The function that describes the height of the rocket in terms of time t is: S(t) = -16t^2 + 112t + 220. Determine the time at which the rocket reaches its maximum height.
30. If an object is propelled upward from a height of 464 feet at an initial velocity of 96 feet per second, then its height after t seconds is given by the equation y(t) = -16t^2 + 96t + 464, where height is in feet. After how many seconds will the object reach a height of 592 feet?

SnapAndSolve AI · Accepted Answer

To find the time at which the rocket reaches its maximum height, we need to find the vertex of the parabola represented by the function S(t) = -16t^2 + 112t + 220. The time at which the maximum height is reached is given by the formula t = -b/(2a), where a = -16 and b = 112.

t = -112 / (2 * -16) = 3.5 seconds.
To find when the object reaches a height of 592 feet, set the equation y(t) = -16t^2 + 96t + 464 equal to 592 and solve for t.

-16t^2 + 96t + 464 = 592

-16t^2 + 96t - 128 = 0

Divide the entire equation by -16:

t^2 - 6t + 8 = 0

Factor the quadratic equation:

(t - 4)(t - 2) = 0

t = 4 or t = 2

Therefore, the object will reach a height of 592 feet after 2 seconds and again after 4 seconds.

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A rocket is propelled upward from the top of a building 220 feet tall at an initial velocity of 112 feet...

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