SOLUTION: 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 ro

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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.
​b) Determine the time at which the rocket reaches its maximum​ height, and the maximum height in feet.
​c) For what time interval will the rocket be more than 457

feet above ground​ level?
​d) After how many seconds will it hit the​ ground?
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
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
-------------
​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
----
​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
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=8228 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 8.52213511761214, 2.85286488238786. Here's your graph:

The smaller value is ascending, the larger descending.
It's at or above between the 2 times.
--------------------
​d) After how many seconds will it hit the​ ground?
h(t) = -16t^2 + 182t + 68 = 0
Solve for t, ignore the negative value.
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