Near the surface of the earth, objects are are subjected to a downward gravitational acceleration denoted by , with value 32 (9.8 ). It is this gravitational acceleration that accounts for the force pulling objects earthward.
Establish a coordinate system with positive upward, measured from ground level. Then, the problem is described by the following.
, ,
As in Example 3.10.2, the position function is found by antidifferentiating twice, paying attention to the initial conditions and . Hence, , with to satisfy the condition , so .
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The position function is , with to satisfy the condition ., so .
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The rock reaches its maximum height when , or at = = .
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The maximum height above ground is = ft, or some 56.25 ft above the top of the cliff.
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The rock reaches ground level when , so the quadratic equation must be solved for . Of course, just the positive time is meaningful here, and that time is approximately seconds after the rock was launched.
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