document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=214250>Question 214250</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A car is parked on a cliff overlooking the ocean<BR>\n" );
document.write( "on an incline that makes an angle of 18.0&#9702;<BR>\n" );
document.write( "below the horizontal. The negligent driver<BR>\n" );
document.write( "leaves the car in neutral, and the emergency<BR>\n" );
document.write( "brakes are defective. The car rolls from rest<BR>\n" );
document.write( "down the incline with a constant acceleration<BR>\n" );
document.write( "of 2.00 m/s2 and travels 43.0 m to the edge of<BR>\n" );
document.write( "the cliff. The cliff is 40.0 m above the ocean.<BR>\n" );
document.write( "The acceleration of gravity is 9.81 m/s2 .<BR>\n" );
document.write( "a) How long is the car in the air? Answer<BR>\n" );
document.write( "in units of s.\r<BR>\n" );
document.write( "\n" );
document.write( "b) What is the car’s position relative to the<BR>\n" );
document.write( "base of the cliff when the car lands in the<BR>\n" );
document.write( "ocean? Answer in units of m.\r<BR>\n" );
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document.write( "whats steps would u take to solve this problem </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #162156 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=162156\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A car is parked on a cliff overlooking the ocean<BR>\n" );
document.write( "on an incline that makes an angle of 18.0&#9702;<BR>\n" );
document.write( "below the horizontal. The negligent driver<BR>\n" );
document.write( "leaves the car in neutral, and the emergency<BR>\n" );
document.write( "brakes are defective. The car rolls from rest<BR>\n" );
document.write( "down the incline with a constant acceleration<BR>\n" );
document.write( "of 2.00 m/s2 and travels 43.0 m to the edge of<BR>\n" );
document.write( "the cliff. The cliff is 40.0 m above the ocean.<BR>\n" );
document.write( "The acceleration of gravity is 9.81 m/s2 .<BR>\n" );
document.write( "a) How long is the car in the air? Answer<BR>\n" );
document.write( "in units of s. <BR>\n" );
document.write( "b) What is the car’s position relative to the<BR>\n" );
document.write( "base of the cliff when the car lands in the<BR>\n" );
document.write( "ocean? Answer in units of m. <BR>\n" );
document.write( "-----------------------------<BR>\n" );
document.write( "s = (at^2)/2<BR>\n" );
document.write( "43 = (2*t^2)/2<BR>\n" );
document.write( "t = sqrt(43) seconds to go the 43 meters<BR>\n" );
document.write( "v = at = 2sqrt(43) m/sec when the car leaves the incline and is airborne.<BR>\n" );
document.write( "v =~ 13.114877 m/sec<BR>\n" );
document.write( "------------<BR>\n" );
document.write( "The vertical component of v is v*sin(18) = -4.05272 m/sec (neg since is down)<BR>\n" );
document.write( "The horizontal part of v is v*cos(18) = 12.473 m/sec<BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "h(t) = -9.81t^2 - 4.05272t + 40<BR>\n" );
document.write( "h(0) = 40 (when it leaves the ground)<BR>\n" );
document.write( "Find t at h = 0 (when it hits the water)<BR>\n" );
document.write( "-9.81t^2 - 4.05272t + 40 = 0<BR>\n" );
document.write( "<TABLE  BORDER=1>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=solve_quadratic_equation.solver>SOLVE quadratic equation (work shown, graph etc)</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <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;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-9.81x%5E2%2B-4.05272x%2B40+=+0 ALIGN=MIDDLE  ALT=\"-9.81x%5E2%2B-4.05272x%2B40+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%28-4.05272%29%5E2-4%2A-9.81%2A40=1586.0245393984 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-4.05272%29%5E2-4%2A-9.81%2A40=1586.0245393984\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=1586.0245393984 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28--4.05272%2B-sqrt%28+1586.0245393984+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--4.05272%2B-sqrt%28+1586.0245393984+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-%28-4.05272%29%2Bsqrt%28+1586.0245393984+%29%29%2F2%5C-9.81+=+-2.23637327194893 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%28-4.05272%29-sqrt%28+1586.0245393984+%29%29%2F2%5C-9.81+=+1.8232519671579 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-4.05272%29-sqrt%28+1586.0245393984+%29%29%2F2%5C-9.81+=+1.8232519671579\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-9.81x%5E2%2B-4.05272x%2B40 ALIGN=MIDDLE  ALT=\"-9.81x%5E2%2B-4.05272x%2B40\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-9.81x%5E2%2B-4.05272x%2B40+=+%28x--2.23637327194893%29%2A%28x-1.8232519671579%29 ALIGN=MIDDLE  ALT=\"-9.81x%5E2%2B-4.05272x%2B40+=+%28x--2.23637327194893%29%2A%28x-1.8232519671579%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -2.23637327194893, 1.8232519671579.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-9.81%2Ax%5E2%2B-4.05272%2Ax%2B40+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-9.81%2Ax%5E2%2B-4.05272%2Ax%2B40+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
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document.write( "t =~ 1.823252 seconds<BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "The horizontal part of v is v*cos(18) = 12.473 m/sec<BR>\n" );
document.write( "12.473 m/sec * 1.823252 seconds =~ 22.741 meters from the base of the cliff<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );