SOLUTION: Please help me solve this problem:A ball is thrown directly upward from an initial height of 200 feet with an initial velocity of 96 feet per second. After t seconds, the height of

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Please help me solve this problem:A ball is thrown directly upward from an initial height of 200 feet with an initial velocity of 96 feet per second. After t seconds, the height of      Log On


   

Question 1034546: Please help me solve this problem:A ball is thrown directly upward from an initial height of 200 feet with an initial velocity of 96 feet per second. After t seconds, the height of the ball above the ground is s(t) = 16t2+ 96t + 200.
a. After how many seconds will the ball reach its maximum height?
b. What was the maximum height?
c. How long will it take before the ball reaches the ground?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The formula for t-value of the vertex ( either max or min ) is:
+-b%2F%282a%29+ when the equation has the form:
+s%28t%29+=+a%2At%5E2+%2B+b%2At+%2B+c+
+a+=+-16+
+b+=+96+
+c+=+200+
--------------
+-b%2F%282a%29+=+-96%2F%282%2A%28-16%29+%29+
+-b%2F%282a%29+=+96%2F32+
+-b%2F%282a%29+=+3+
So, +t=3+. Now plug this value back into equation to get s-value
+s%28t%29+=+-16t%5E2+%2B+96t+%2B+200+
+s%283%29+=+-16%2A3%5E2+%2B+96%2A3+%2B+200+
+s%283%29+=+-16%2A9+%2B+288+%2B+200+
+s%283%29+=+-144+%2B+488+
+s%283%29+=+344+
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The ball reaches the ground when +h+=+0+
+0+=+-16t%5E2+%2B+96t+%2B+200+
+0+=+-2t%5E2+%2B+12t+%2B+25+
Use quadratic formula
+t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+t+=+%28-12+%2B-+sqrt%28+12%5E2-4%2A%28-2%29%2A25+%29%29%2F%282%2A%28-2%29%29+
+t+=+%28-12+%2B-+sqrt%28+144+%2B+200%29%2F%28-4+%29%29+
+t+=+%28-12+%2B-+sqrt%28+344%29%2F%28-4+%29%29+
+t+=+%28+-12+-+18.5472+%29+%2F+%28-4%29+
+t+=+%28+-30.5472+%29+%2F+%28-4%29+
+t+=+7.6368+
(a)
In 3 sec the ball reaches maximum height
(b)
The maximum height is 344 ft
(c)
The ball hits the ground in 7.6368 sec
------------------------------------
Here's the plot:
+graph%28+500%2C+500%2C+-10%2C+10%2C+-40%2C+400%2C+-16x%5E2+%2B+96x+%2B+200+%29+