document.write( "Question 66214: I NEED HELP PLEASE!
\n" ); document.write( "Suppose a baseball is shot up from the ground straight up with an initial velocity of 32 feet per second. A function can be created by expressing distance above the ground, s, as a function of time, t. This function is s = -16t2 + v0t + s0
\n" ); document.write( "• 16 represents ½g, the gravitational pull due to gravity (measured in feet per second 2).
\n" ); document.write( "• v0 is the initial velocity (how hard do you throw the object, measured in feet per second).
\n" ); document.write( "• s0 is the initial distance above ground (in feet). If you are standing on the ground, then s0 = 0.
\n" ); document.write( "What is the function that describes this problem?
\n" ); document.write( "The ball will be how high above the ground after 1 second?
\n" ); document.write( "How long will it take to hit the ground?
\n" ); document.write( "What is the maximum height of the ball? \n" ); document.write( "
Algebra.Com's Answer #46937 by Earlsdon(6294)\"\" \"About 
You can put this solution on YOUR website!
Given:
\n" ); document.write( "\"s+=+-16t%5E2%2BVot%2BHo\" and Vo = 32 ft/sec and Ho = 0
\n" ); document.write( "1) Write the function for this problem. This can be done by writing the above equation in function form and substituting the given initial conditions for V0 and Ho.
\n" ); document.write( "\"s%28t%29+=+-16t%5E2%2B32t\"\r
\n" ); document.write( "\n" ); document.write( "2) The height of the ball after 1 second can be found by substituting t = 1 into the function s(t) and solving for s.
\n" ); document.write( "\"s%281%29+=+-16%281%29%5E2%2B32%281%29\"
\n" ); document.write( "\"s%281%29+=+-16%2B32\"
\n" ); document.write( "s(1) = 16}}}
\n" ); document.write( "The height after 1 second will be 16 feet above the ground.\r
\n" ); document.write( "\n" ); document.write( "3) To find out how long it will take to hit the ground (s = 0), set the function s(t) = 0 and solve for t.
\n" ); document.write( "\"s%28t%29+=+-16t%5E2%2B32t\"
\n" ); document.write( "\"0+=+-16t%5E2%2B32t\" Simplify and solve for t. Factor a t.
\n" ); document.write( "\"0+=+t%28-16t%2B32%29\" Apply the zero product principle:
\n" ); document.write( "\"t+=+0\" and \"-16t+%2B+32+=+0\"
\n" ); document.write( "\"t+=+0\" is one solution and this represents the initial condition when the ball is first thrown.
\n" ); document.write( "\"-16t%2B32+=+0\" Subtract 32 from both sides.
\n" ); document.write( "\"-16t+=+-32\" Divide both sides by -16.
\n" ); document.write( "\"t+=+2\" is the other solution and this represents the terminal condition when the ball hits the ground after falling.\r
\n" ); document.write( "\n" ); document.write( "4) The maximum height of the ball occurs at the vertex of the curve (a parabola) represented by the function: \"s%28t%29+=+-16t%5E2%2B32t\"
\n" ); document.write( "The vertex of this parabola is a maximum because the curve opens downward as indicated by the negative coefficient of the t^2 term.
\n" ); document.write( "The t-coordinate of the vertex is given by:
\n" ); document.write( "\"t+=+%28-b%29%2F2a\" The a and b come from: \"ax%5E2%2Bbx%2Bc+=+0\" the general form for the quadratic equation. In this case, a = -16 and b = 32, so:
\n" ); document.write( "\"t+=+%28-32%29%2F2%28-16%29\"
\n" ); document.write( "\"t+=+1\" The maximum height occurs at time t = 1 second. To find the height in feet, substitute t = 1 into the function s(t) and solve for s.
\n" ); document.write( "\"s%281%29+=+-16%281%29%5E2+%2B+32%281%29\" Simplify.
\n" ); document.write( "\"s%281%29+=+-16%2B32\"
\n" ); document.write( "\"s%281%29+=+16\" The maximum height in feet.
\n" ); document.write( "Here's a graph of the function:
\n" ); document.write( "\"graph%28300%2C200%2C-5%2C5%2C-5%2C20%2C-16x%5E2%2B32x%29\"
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