QuestionFind the maximum height of the shot modeled by and its distance from the release point.
Studdy Solution
STEP 1
Assumptions1. The height of the shot, , is modeled by the equation .
. The variable represents the shot's horizontal distance, in feet, from its point of release.
3. We are looking for the maximum height of the shot and the distance from the point of release at which this occurs.
STEP 2
The maximum height of the shot occurs at the vertex of the parabola represented by the equation . Since the equation is in the form , the -coordinate of the vertex can be found using the formula .
STEP 3
Plug in the values for and from the equation to find the -coordinate of the vertex.
STEP 4
Calculate the -coordinate of the vertex.
STEP 5
Now that we have the -coordinate of the vertex, we can find the maximum height of the shot by substituting into the equation .
STEP 6
Calculate the maximum height of the shot.
The maximum height of the shot is9.8 feet, which occurs30 feet from the point of release.
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