document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=985203>Question 985203</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I would really appreciate if someone would walk me through this problem in detail. I am stuck on this question. Thank you sooo much for your help!!!!!\r<BR>\n" );
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document.write( "Near the surface of the earth, assuming negligible resistance from the air, the height in feet of a falling object is modeled well by the equation y = h &#8722; 16t^2 , where y is the height of the object, t is the number of seconds the object has been falling, and h is the height from which the object was dropped. (On your calculators, you will graph y for h and x for t). \r<BR>\n" );
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document.write( "a) If an iron ball were dropped from the Washington Monument, which is 555 feet high, how far above the ground would the ball be after 2 seconds of falling? How long would it take for the ball to hit the ground? \r<BR>\n" );
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document.write( "b) Due to air resistance, a falling bag of corn chips will not gain speed as rapidly as a falling iron ball. Cal Elayo, a student of science, found that the descent of a falling bag of chips is modeled well by the equation y = h &#8722; 2.5t^2 . In an historic experiment, Cal dropped a bag of chips from a point halfway up the Monument, while a friend simultaneously dropped the iron ball from the top. After how many seconds did the ball overtake the bag of chips? \r<BR>\n" );
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document.write( "c) Graph the equations y = 277.5 &#8722; 2.5t^2 and y = 555 &#8722;16t^2 on the same system of axes. Calculate the y- and t-intercepts of both curves. What is the meaning of these numbers? Notice that the curves intersect. What is the meaning of the intersection point?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #606177 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=606177\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> y = h &#8722; 16t^2 , where y is the height of the object, t is the number of seconds the object has been falling, and h is the height from which the object was dropped<BR>\n" );
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document.write( "a) y = 555 - 16(2^2)<BR>\n" );
document.write( "y = 555 - 64 = 491,<BR>\n" );
document.write( "--the iron ball is 491 feet above the ground after 2 seconds<BR>\n" );
document.write( "0 = 555 - 16t^2<BR>\n" );
document.write( "16t^2 = 555<BR>\n" );
document.write( "t^2 = 555 / 16<BR>\n" );
document.write( "t = square root(555 / 16) = square root(555) / 4 = 5.889609495 approx 5.9<BR>\n" );
document.write( "--it takes 5.9 seconds for the iron ball to hit the ground<BR>\n" );
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document.write( "b)  y = h &#8722; 2.5t^2, 555/2 = 277.5<BR>\n" );
document.write( "set equations a and b equal to each other<BR>\n" );
document.write( "555 - 16t^2 = 277.5 - 2.5t^2<BR>\n" );
document.write( "13.5t^2 = 277.5<BR>\n" );
document.write( "t^2 = 277.5 / 13.5 = 20.555555556<BR>\n" );
document.write( "t = square root(20.555555556) = 4.533823503<BR>\n" );
document.write( "--in 4.5 seconds the ball will overtake the bag of chips<BR>\n" );
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document.write( "c) y = 555 - 16t^2 (red line), y = 277.5 - 2.5t^2 (green line)<BR>\n" );
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document.write( "calculate y intercept by setting t = 0<BR>\n" );
document.write( "calculate t intercept by setting y = 0<BR>\n" );
document.write( "--y = 555 - 16t^2<BR>\n" );
document.write( "y intercept is (555, 0)<BR>\n" );
document.write( "--0 = 555 - 16t^2<BR>\n" );
document.write( "t = 5.9<BR>\n" );
document.write( "t intercept is (0, 5.9)<BR>\n" );
document.write( "--y = 277.5 - 2.5t^2<BR>\n" );
document.write( "y intercept is (277.5, 0)<BR>\n" );
document.write( "--0 = 277.5 - 2.5t^2<BR>\n" );
document.write( "t = 10.535653753 approx 10.5<BR>\n" );
document.write( "t intercept is (0, 10.5)<BR>\n" );
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document.write( "--y intercept is the height above the ground, t intercept is the time in seconds it takes the object to reach the ground<BR>\n" );
document.write( "--the intersection point gives us the height above the ground when the objects over take each other and the time it takes for that to happen\r<BR>\n" );
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