Question 1200687
A toy rocket is launched from the top of a building 68 feet tall at an initial velocity of 182 feet per second.
​a) Give the function that describes the height of the rocket in terms of time t.
h(t) = h(t) = -16t^2 + 182t + 68
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​b) Determine the time at which the rocket reaches its maximum​ height, and the maximum height in feet.
The max of the parabola is at t = -b/2a
t = -182/-32 = 5.6875 seconds
h(5.6875) = 585.5625 ft
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​c) For what time interval will the rocket be more than 457 feet above ground​ level?
h(t) = -16t^2 + 182t + 68 = 457
16t^2 - 182t + 389 = 0
*[invoke solve_quadratic_equation 16,-182,389]
The smaller value is ascending, the larger descending.
It's at or above between the 2 times.
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​d) After how many seconds will it hit the​ ground?
h(t) = -16t^2 + 182t + 68 = 0
Solve for t, ignore the negative value.