document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=139518>Question 139518</A>: <I><SPAN STYLE=\"word-break: break-all;\"> hello....I am stumped...hope you can help...Question: Assume Joe Ball hits a major league pop-up (straight upward) on a Johnny Bench 90mph pitch. The function that describes the ball's height (in feet/second) is: h(t) = -16t^2+132t h(t) is height, t = is seconds...How many seconds for the ball to go up and back down? How high does the ball go? I came up with answers 4.125 for ball to go up and down and 272.25 feet for how high ball goes up (correct??)...but here's the stumper: it's now asking to repeat problem using planet Mercury. How do I complete this? (FYI, Mercury is 38% of Earth)....Hope you can help and show me the correct formula and answers..Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #101713 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=101713\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's look at part I of the problem:<BR>\n" );
document.write( "I)<BR>\n" );
document.write( "a) How many seconds for the ball to go up and down?<BR>\n" );
document.write( "In other words, how many seconds for the ball to return to the ground?<BR>\n" );
document.write( "Starting with the given formula:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29+=+-16t%5E2%2Bv%5B0%5Dt%2Bh%5B0%5D ALIGN=MIDDLE  ALT=\"h%28t%29+=+-16t%5E2%2Bv%5B0%5Dt%2Bh%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > where: <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v%5B0%5D+=+132 ALIGN=MIDDLE  ALT=\"v%5B0%5D+=+132\"   DISABLED_style= \"max-width:90%; height:auto;\" >ft/sec This is the initial upward velocity.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5B0%5D+=+0 ALIGN=MIDDLE  ALT=\"h%5B0%5D+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >  This is the initial height.<BR>\n" );
document.write( "So we have:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29+=+-16t%5E2%2B132t ALIGN=MIDDLE  ALT=\"h%28t%29+=+-16t%5E2%2B132t\"   DISABLED_style= \"max-width:90%; height:auto;\" > and you want to find the time, t, when h = 0: <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+-16t%5E2%2B132t ALIGN=MIDDLE  ALT=\"0+=+-16t%5E2%2B132t\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor a t from the right-hand side.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+t%28-16t%2B132%29 ALIGN=MIDDLE  ALT=\"0+=+t%28-16t%2B132%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Apply the zero product rule: If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Ab+=+0 ALIGN=MIDDLE  ALT=\"a%2Ab+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > then either <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+0 ALIGN=MIDDLE  ALT=\"a+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+0 ALIGN=MIDDLE  ALT=\"b+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or both. <BR>\n" );
document.write( "Add 16t to both sides. So...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+0 ALIGN=MIDDLE  ALT=\"t+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16t%2B132+=+0 ALIGN=MIDDLE  ALT=\"-16t%2B132+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16t+%2B+132+=+0 ALIGN=MIDDLE  ALT=\"-16t+%2B+132+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 16t to both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=132+=+16t ALIGN=MIDDLE  ALT=\"132+=+16t\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 16.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+8.25 ALIGN=MIDDLE  ALT=\"t+=+8.25\"   DISABLED_style= \"max-width:90%; height:auto;\" >seconds.<BR>\n" );
document.write( "The ball returns to the ground in 8.25 seconds.<BR>\n" );
document.write( "b) How high does the ball go?<BR>\n" );
document.write( "You'll need to find the value of t at the vertex of the parabola described by the given equation.  This is given by:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+-b%2F2a ALIGN=MIDDLE  ALT=\"t+=+-b%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" > The a and b come from: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc+=+0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and in this case, a = -16 and b = 132.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-132%29%2F2%28-16%29 ALIGN=MIDDLE  ALT=\"t+=+%28-132%29%2F2%28-16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+4.125 ALIGN=MIDDLE  ALT=\"t+=+4.125\"   DISABLED_style= \"max-width:90%; height:auto;\" > seconds.  This is the time at which the ball reaches its maximum height.  Substitute this value of t into the given equation and solve for h to find the maximum height.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%284.125%29+=+-16%284.125%29%5E2%2B132%284.125%29 ALIGN=MIDDLE  ALT=\"h%284.125%29+=+-16%284.125%29%5E2%2B132%284.125%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%284.125%29+=+-272.5%2B544.5 ALIGN=MIDDLE  ALT=\"h%284.125%29+=+-272.5%2B544.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%284.125%29+=+272.25 ALIGN=MIDDLE  ALT=\"h%284.125%29+=+272.25\"   DISABLED_style= \"max-width:90%; height:auto;\" > feet. Which is precisely what you got.<BR>\n" );
document.write( "II) For this problem to be solved for the planet Mercury whose gravitational force is 38% that of earth's, let's look at the original formula for the height of an object propelled upwards:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29+-+%281%2F2%29gt%5E2%2Bv%5B0%5Dt%2Bh%5B0%5D ALIGN=MIDDLE  ALT=\"h%28t%29+-+%281%2F2%29gt%5E2%2Bv%5B0%5Dt%2Bh%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Here, the acceleration due to gravity is: g = 32 ft/second squared for earth.<BR>\n" );
document.write( "For Mercury, g = 0.38(32)ft/second squared = 12.16 feet/second squared.<BR>\n" );
document.write( "So the formula for the planet Mercury becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29+=+-%281%2F2%2912.16t%5E2%2Bv%5B0%5D%2Bh%5B0%5D ALIGN=MIDDLE  ALT=\"h%28t%29+=+-%281%2F2%2912.16t%5E2%2Bv%5B0%5D%2Bh%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29+=+-6.08t%5E2%2Bv%5B0%5Dt%2Bh%5B0%5D ALIGN=MIDDLE  ALT=\"h%28t%29+=+-6.08t%5E2%2Bv%5B0%5Dt%2Bh%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > This is the formula you would use to solve the second part of the problem.<BR>\n" );
document.write( "a)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29+=+-6.08t%5E2%2B132t ALIGN=MIDDLE  ALT=\"h%28t%29+=+-6.08t%5E2%2B132t\"   DISABLED_style= \"max-width:90%; height:auto;\" > Set h = 0 and solve for t.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+-6.08t%5E2%2B132t ALIGN=MIDDLE  ALT=\"0+=+-6.08t%5E2%2B132t\"   DISABLED_style= \"max-width:90%; height:auto;\" > So...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+0 ALIGN=MIDDLE  ALT=\"t+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+132%2F6.08 ALIGN=MIDDLE  ALT=\"t+=+132%2F6.08\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+21.71 ALIGN=MIDDLE  ALT=\"t+=+21.71\"   DISABLED_style= \"max-width:90%; height:auto;\" > seconds.  This is the time at which the ball returns to the ground on Mercury.<BR>\n" );
document.write( "The time to reach its maximum height is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+-b%2F2a ALIGN=MIDDLE  ALT=\"t+=+-b%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" > where: a = -6.06 and b = 132.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+-%28132%2F2%28-6.08%29%29 ALIGN=MIDDLE  ALT=\"t+=+-%28132%2F2%28-6.08%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+10.86 ALIGN=MIDDLE  ALT=\"t+=+10.86\"   DISABLED_style= \"max-width:90%; height:auto;\" >seconds. Substitute this into the formula for Mercury:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%2810.86%29+=+-6.08%2810.86%29%5E2%2B132%2810.86%29 ALIGN=MIDDLE  ALT=\"h%2810.86%29+=+-6.08%2810.86%29%5E2%2B132%2810.86%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%2810.86%29+=+-66%2B1433.52 ALIGN=MIDDLE  ALT=\"h%2810.86%29+=+-66%2B1433.52\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%2810.86%29+=+1367.52 ALIGN=MIDDLE  ALT=\"h%2810.86%29+=+1367.52\"   DISABLED_style= \"max-width:90%; height:auto;\" >feet. This is the maximum height attained by the ball on Mercury.\r<BR>\n" );
document.write( "\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );