SOLUTION: Pocahontas wants to impress John Smith by doing a cliff dive the height of the cliff is 72 feet from the water. she reaches a maximum height at 75 feet in half a second how long

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: Pocahontas wants to impress John Smith by doing a cliff dive the height of the cliff is 72 feet from the water. she reaches a maximum height at 75 feet in half a second how long       Log On


   

Question 1101707: Pocahontas wants to impress John Smith by doing a cliff dive the height of the cliff is 72 feet from the water. she reaches a maximum height at 75 feet in half a second how long does it take her to hit the water.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The equation would be:
+h%28t%29+=+-16t%5E2+%2B+k%2At+%2B+72+
If +t=0+, then +h%280%29+=+72+ ft
as it should
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You are given the maximum height at
( t,h ) = ( .5, 75 )
+75+=+-16%2A.5%5E2+%2B+k%2A.5+%2B+72+
+75+=+-4+%2B+.5k+%2B+72+
+3+=+-4+%2B+.5k+
+.5k+=+7+
+k+=+14+
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So the equation is:
+h%28t%29+=+-16t%5E2+%2B+14t+%2B+72+
When she hits the water, +h%28t%29+=+0+
+-16t%5E2+%2B+14t+%2B+72+=+0+
+-8t%5E2+%2B+7t+%2B+36+=+0+
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Use the quadratic formula
+t+=+%28+-b+%2B-sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%28+2a+%29+
+a+=+-8+
+b+=+7+
+c+=+36+
+t+=+%28+-7+%2B-sqrt%28+7%5E2+-+4%2A%28-8%29%2A36+%29%29+%2F+%282%2A%28-8%29%29+
+t+=+%28+-7+%2B-sqrt%28+49+%2B+1152+%29%29+%2F+%28-16%29+
+t+=+%28+-7+%2B-sqrt%28+1201+%29%29+%2F+%28+-16+%29+
+t+=+%28+-7+-+34.655+%29+%2F+%28-16%29+
+t+=+41.655%2F16+
+t+=+2.603+
She hits the water in 2.603 sec
Get a 2nd opinion if needed
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check:
Here's the plot:
+graph%28+400%2C+400%2C+-1%2C+4%2C+-10%2C+90%2C+-16x%5E2+%2B+14x+%2B+72+%29+