document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1165760>Question 1165760</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A bullet is fired from a gun and made a projectile motion. The trace of the path of the bullet is mathematically expressed as d = 60t — 4t2, where d is the distance in meters of the bullet from the ground in t seconds.\r<BR>\n" );
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document.write( "a. What is the distance of the bullet from the ground after 2 seconds (s)?\r<BR>\n" );
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document.write( "b. At what time will the bullet reach a height of 200 m?\r<BR>\n" );
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document.write( "c. What maximum distance from the ground does the bullet reach?\r<BR>\n" );
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document.write( "d. After how many seconds does the bullet reach its highest point?\r<BR>\n" );
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document.write( "e. At what time will the bullet hit the ground? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #790207 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=790207\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> d=60t-4t^2<BR>\n" );
document.write( "so d(2)=120-16=104 m.\r<BR>\n" );
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document.write( "200=-4t^2+60t<BR>\n" );
document.write( "so 4t^2-60t=200=0<BR>\n" );
document.write( "and<BR>\n" );
document.write( "t^2-15t+50=0, dividing by 4<BR>\n" );
document.write( "(t-10)(t-5)=0<BR>\n" );
document.write( "so at t = 5 and 10 seconds\r<BR>\n" );
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document.write( "maximum distance up is at the vertex or t=-b/2a That is 60/8 or 7.5 seconds.<BR>\n" );
document.write( "d(7.5)=450-225=225 m\r<BR>\n" );
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document.write( "It hits the ground after 15 seconds, twice the time it takes to reach the highest point.<BR>\n" );
document.write( "one could also do 4t^2-60t=0<BR>\n" );
document.write( "t^2-15t=0<BR>\n" );
document.write( "t(t-15)=0<BR>\n" );
document.write( "t=0 (start) and t=15 seconds.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-10%2C20%2C-100%2C500%2C60x-4x%5E2%2C200%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-10%2C20%2C-100%2C500%2C60x-4x%5E2%2C200%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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