document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1142427>Question 1142427</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A Weather sensor is shot from a platform into the air and allowed to fall back to the ground. Its height in meters is given by the equation h= -49t^2 + 18t + 5, where t is the time in seconds. <BR>\n" );
document.write( "a) What is the maximum height of the sensor, and at what time does it occur?<BR>\n" );
document.write( "b) When does the Rocket return to the ground?<BR>\n" );
document.write( "c) At what times is the sensor 15 meter above the ground?<BR>\n" );
document.write( "d) How high is the sensor after 1.5 seconds? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #763124 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=763124\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A Weather sensor is shot from a platform into the air and allowed to fall back to the ground. Its height in meters is given by the equation h= -49t^2 + 18t + 5, where t is the time in seconds. <BR>\n" );
document.write( "a) What is the maximum height of the sensor, and at what time does it occur?<BR>\n" );
document.write( "Max height is the vertex of the parabola, at t = -b/2a<BR>\n" );
document.write( "t = -18/-98 = 9/49 seconds.<BR>\n" );
document.write( "h(t) = -49t^2 + 18t + 5<BR>\n" );
document.write( "h(9/49) = -49*(81/2401) + 18*9/49 + 5<BR>\n" );
document.write( "= -81/49 + 162/49 + 245/49<BR>\n" );
document.write( "= 336/49 = 48/7 meters<BR>\n" );
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document.write( "b) When does the Rocket return to the ground?<BR>\n" );
document.write( "When h(t) = 0<BR>\n" );
document.write( "-49t^2 + 18t + 5 = 0<BR>\n" );
document.write( "Solve for t<BR>\n" );
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document.write( "c) At what times is the sensor 15 meter above the ground?<BR>\n" );
document.write( "At no time.<BR>\n" );
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document.write( "d) How high is the sensor after 1.5 seconds?<BR>\n" );
document.write( "Find h(1.5)<BR>\n" );
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document.write( "The function is probably h(t) = -4.9t^2 + 18t + 5, not 49t^2<BR>\n" );
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document.write( "If so, do the same calculations using 4.9.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );