document.write( "Question 24543: suppose you throw a basebal straight up at a velocity of 64 ft per second.A funtion can be created by expressing distance above the ground, s , as a function of time, t. this function is \"s=-16t%5E2=v0t%2Bs0\" (<\n" ); document.write( "\n" ); document.write( "16 represents 1/2 g,gravitational pull in ft per second^2.
\n" ); document.write( "v0is the inital velocity in ft per second
\n" ); document.write( "so is intial distance above ground in ft. if you are stading on the ground , then s0= zero.\r
\n" ); document.write( "\n" ); document.write( "what is the function descibing this problem?\r
\n" ); document.write( "\n" ); document.write( "how high above the ground will the ball be after one sec?\r
\n" ); document.write( "\n" ); document.write( "how long will it take to hit the ground?\r
\n" ); document.write( "\n" ); document.write( "what is the maximum height and time attained by the ball?\r
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Algebra.Com's Answer #13085 by Earlsdon(6294)\"\" \"About 
You can put this solution on YOUR website!
Hmmm...I think I have answered this one previously. Anyway, here it is again.
\n" ); document.write( "The equation is correct:
\n" ); document.write( "\"s%28t%29+=+-16t%5E2+%2Bvot+%2B+ho\"
\n" ); document.write( "\"s%28t%29+=+-16t%5E2+%2B+64t\" This is the function describing the problem. In words, the height (s) is a quadratic function of time (t) with initial velocity of 64 ft/sec and an initial height of zero.\r
\n" ); document.write( "\n" ); document.write( "After 1 second (t=1), the height of the baseball will be:
\n" ); document.write( "\"s%281%29+=+-16%281%29%5E2+%2B+64%281%29\"
\n" ); document.write( "\"s%281%29+=+-16%2B+64\"
\n" ); document.write( "\"s%281%29+=+48\" The height will be 48 feet after 1 second.\r
\n" ); document.write( "\n" ); document.write( "Find when the baseball will hit the ground (s=0) by setting the function s(t) = 0 and solving for t.
\n" ); document.write( "\"-16t%5E2+%2B+64t+=+0\" Factor out a t.
\n" ); document.write( "\"t%28-16t+%2B+64%29+=+0\" Divide both sides by t.
\n" ); document.write( "\"-16t+%2B+64+=+0\" Subtract 64 from both sides.
\n" ); document.write( "\"-16t+=+-64\" Divide both sides by -16
\n" ); document.write( "\"t+=+4\" The baseball will return to ground in 4 seconds.\r
\n" ); document.write( "\n" ); document.write( "The maximum height and time is found by finding the location of the vertex of this parabola.
\n" ); document.write( "Since the parabola opens downward, the vertex will be at the maximum point of the vertex and will represent the maximum height attained by the baseball.
\n" ); document.write( "The x-coordinate (or, in this problem, the t-coordinate) is given by:
\n" ); document.write( "\"t+=+-b%2F2a\"
\n" ); document.write( "The a and b come from the standard form of the quadratic equation: \"ax%5E2+%2B+bx+%2B+c+=+0\"
\n" ); document.write( "In this case, a = -16, b = 64, and c = 0\r
\n" ); document.write( "\n" ); document.write( "\"t+=+-64%2F2%28-16%29\"
\n" ); document.write( "\"t+=+2\" The maximum height of the baseball will be attained in 2 seconds.\r
\n" ); document.write( "\n" ); document.write( "To find this maximum eight, substitute t=2 into the original function and solve for s.
\n" ); document.write( "\"S%282%29+=+-16%282%29%5E2+%2B+64%282%29\"
\n" ); document.write( "\"s%282%29+=+-16%284%29+%2B+128\"
\n" ); document.write( "\"s%282%29+=+-64+%2B+128\"
\n" ); document.write( "\"s%282%29+=+64\" The maximum height attained by the baseball is 64 feet.
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