document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1002246>Question 1002246</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi,\r<BR>\n" );
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document.write( "I would just like to say thank you for your help in advanced. \r<BR>\n" );
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document.write( "My question is as follows:\r<BR>\n" );
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document.write( "The arm of an indrustrial robot starts at a speed Vo and drops 34.8 cm in 4.28 seconds, at constant acceleration a. Its motion is described by \r<BR>\n" );
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document.write( "s= Vot + (at^2)/2 <BR>\n" );
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document.write( "34.8 = 4.28Vo + [a(4.28)^2]/2 \r<BR>\n" );
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document.write( "In another trial the arm is found to drop 58.3 cm in 5.57 seconds, with the same initial speed and acceleration. Find Vo and a. \r<BR>\n" );
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document.write( "Thank you \r<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 #619261 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=619261\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The arm of an indrustrial robot starts at a speed Vo and drops 34.8 cm in 4.28 seconds, at constant acceleration a. Its motion is described by<BR>\n" );
document.write( "s= (Vo)t + (at^2)/2<BR>\n" );
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document.write( "34.8 = 4.28Vo + [a(4.28)^2]/2<BR>\n" );
document.write( "In another trial the arm is found to drop 58.3 cm in 5.57 seconds, with the same initial speed and acceleration. Find Vo and a. \r<BR>\n" );
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document.write( "you get s = 34.8 and t = 4.28\r<BR>\n" );
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document.write( "formula becomes:\r<BR>\n" );
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document.write( "34.8 = 4.28(Vo) + (a*4.28^2)/2\r<BR>\n" );
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document.write( "you have another trial where s = 58.3 and t = 5.57\r<BR>\n" );
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document.write( "formula becomes:\r<BR>\n" );
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document.write( "58.3 = 5.57(Vo) + (a*5.57^2)/2\r<BR>\n" );
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document.write( "since Vo and a remain the same in both equations, you have 2 equations that need to be solved simultaneously.\r<BR>\n" );
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document.write( "those equations are:\r<BR>\n" );
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document.write( "34.8 = 4.28(Vo) + (a*4.28^2)/2<BR>\n" );
document.write( "58.3 = 5.57(Vo) + (a*5.57^2)/2\r<BR>\n" );
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document.write( "simplify these equations to get:\r<BR>\n" );
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document.write( "34.8 = 4.28(Vo) + 9.1592(a)<BR>\n" );
document.write( "58.3 = 5.57(Vo) + 15.51245(a)\r<BR>\n" );
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document.write( "multiply both sides of the first equation by 5.57 and multiply both sides of the second equation  by 4.28 to get:\r<BR>\n" );
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document.write( "193.836 = 23.8396(Vo) + 51.016744(a)<BR>\n" );
document.write( "249.524 = 23.8396(Vo) + 66.393286\r<BR>\n" );
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document.write( "subtract the first equation from the second equation to get:\r<BR>\n" );
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document.write( "55.688 = 0 + 15.376542(a)\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "55.688 = 15.376542(a)\r<BR>\n" );
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document.write( "solve for a to get:\r<BR>\n" );
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document.write( "a = 3.621620518\r<BR>\n" );
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document.write( "go back to either original equation and solve for Vo to get:\r<BR>\n" );
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document.write( "Vo = .3805732134\r<BR>\n" );
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document.write( "that's your solution.\r<BR>\n" );
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document.write( "substitute those values for a and Vo in both your original equations and you will get:\r<BR>\n" );
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document.write( "34.8 = 4.28(.38057342134) + 9.1592(3.621620518) = 34.8<BR>\n" );
document.write( "58.3 = 5.57(.38057342134) + 15.51245(3.621620518) = 58.3\r<BR>\n" );
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document.write( "your solution is confirmed as good.\r<BR>\n" );
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document.write( "your solution is:\r<BR>\n" );
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document.write( "Vo = .38057342134<BR>\n" );
document.write( "a = 3.621620518\r<BR>\n" );
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document.write( "you could also have solved both of these equations graphically.\r<BR>\n" );
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document.write( "you would do this as shown below:\r<BR>\n" );
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document.write( "the 2 equations are:\r<BR>\n" );
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document.write( "34.8 = 4.28(Vo) + (a*4.28^2)/2<BR>\n" );
document.write( "58.3 = 5.57(Vo) + (a*5.57^2)/2\r<BR>\n" );
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document.write( "solve for Vo in both equations to get:\r<BR>\n" );
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document.write( "Vo = (34.8 - (a*4.28^2)/2)/4.28<BR>\n" );
document.write( "Vo = (58.3 - (a*5.57^2)/2)/5.57\r<BR>\n" );
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document.write( "set y = Vo and set x = a and the equations become:\r<BR>\n" );
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document.write( "y = (34.8 - (x*4.28^2)/2)/4.28<BR>\n" );
document.write( "y = (58.3 - (x*5.57^2)/2)/5.57\r<BR>\n" );
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document.write( "graph both these equations as is and then find the intersection of both equations on the graph.\r<BR>\n" );
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document.write( "you will get the following graphical solution:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2015/110906.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "the intersection point is shown.\r<BR>\n" );
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document.write( "x = a<BR>\n" );
document.write( "y = Vo\r<BR>\n" );
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document.write( "x = 3.622<BR>\n" );
document.write( "a = .381\r<BR>\n" );
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document.write( "these are the same solutions obtained by formula except they are rounded to 3 decimal digits.\r<BR>\n" );
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