SOLUTION: Water gets sprayed out of a water gun and follows a parabolic path described by h=-4.9t^2+8t+1.5 What is the maximum height of the water and when is it reached?

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Water gets sprayed out of a water gun and follows a parabolic path described by h=-4.9t^2+8t+1.5 What is the maximum height of the water and when is it reached?      Log On


   

Question 797050: Water gets sprayed out of a water gun and follows a parabolic path described by
h=-4.9t^2+8t+1.5 What is the maximum height of the water and when is it reached?
Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Water gets sprayed out of a water gun and follows a parabolic path described by
h=-4.9t^2+8t+1.5 What is the maximum height of the water and when is it reached?
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Max occurs when t = -b/(2a) = -8/(2*-4.9) = 0.8163 seconds
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Max height = h(0.8163) = 4.7653 meters
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Cheers,
Stan H.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+h=-4.9t%5E2%2B8t%2B1.5+
If the form of the equation is
+f%28x%29+=+ax%5E2+%2B+bx+%2B+c+, then the x-coordinate of
the maximum or minimum is at +x%5Bmax%5D+=+-b%2F%282a%29+
In your problem,
+a+=+-4.9+
+b+=+8+
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+t%5Bmax%5D+=+-8%2F%282%2A%28-4.9%29%29+
+t%5Bmax%5D+=+8%2F9.8+
+t%5Bmax%5D+=+.8163+
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Now find +h%5Bmax%5D+
+h%5Bmax%5D+=-4.9%2A.8163%5E2%2B8%2A.8163%2B1.5+
+h%5Bmax%5D+=+-4.9%2A.6663+%2B+6.5304+%2B+1.5+
+h%5Bmax%5D+=+-3.2651+%2B+8.0304+
+h%5Bmax%5D+=+4.765+
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Here's the plot:
+graph%28+400%2C+400%2C+-3%2C+3%2C+-6%2C+6%2C+-4.9x%5E2+%2B+8x+%2B+1.5+%29+