SOLUTION: Jacob is standing at the top of an 80 ft-high cliff and throws a rock upwards at 64 ft/sec Write a model that describes the trajectory of the rock. How many seconds until the

Question 1150174: Jacob is standing at the top of an 80 ft-high cliff and throws a rock upwards at 64 ft/sec
Write a model that describes the trajectory of the rock.
How many seconds until the max height is reached?
What will be the maximum height?
How many seconds until the rock hits the ground?
How high is the rock after 3 seconds?
Found 2 solutions by Edwin McCravy, ikleyn:
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
Write a model that describes the trajectory of the rock.

How many seconds until the max height is reached?
The easiest way is to use the vertex formula, for the maximum height is reached at the vertex which has t coordinate. We put the quadratic in standard form at²+bt+c It take 4 seconds for the rock to get back even with Jacob, so it reached its maximum height in half that time or 2 seconds. But the vertex formula is the easiest.
What will be the maximum height?
The rock's maximum height is reached when t=2 seconds.
How many seconds until the rock hits the ground?
That's when h(t) = 0 We set h(t)=0 and solve for t Divide through by 16 Ignore the negative answer. 5 seconds.
How high is the rock after 3 seconds?
This is h(3) Edwin

Answer by ikleyn(52778)   (Show Source): You can put this solution on YOUR website!
.

In addition to the remarkable solution by Edwin, see also the lessons
    - Problem on a projectile moving vertically up and down
    - Problem on an arrow shot vertically upward
    - Problem on a ball thrown vertically up from the top of a tower
    - Problem on a toy rocket launched vertically up from a tall platform
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The referred lessons are the part of this textbook under the topic "Projectiles launched/thrown and moving vertically up and dawn".

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