document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=193832>Question 193832</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the height, of a ball, above ground using the following information. <BR>\n" );
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document.write( "wait 3 seconds, velocity is 45 ft/sec, initial height above ground is 10 ft\r<BR>\n" );
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document.write( "		1 ft<BR>\n" );
document.write( "		3 ft<BR>\n" );
document.write( "		13 ft<BR>\n" );
document.write( "		4 ft </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #145535 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=145535\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "<b>This is the same problem I solved earlier, just with slightly different numbers.  You should be able to make the appropriate substitutions.</b>\r<BR>\n" );
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document.write( "Technically speaking, you cannot answer this question from the information given.  That is because you haven't actually given the initial velocity.  Yes, I know that you said the initial velocity is 55 ft/sec, but that is only part of the story.  55 ft/sec is a speed, i.e. a scalar quantity.  Velocity is a vector quantity and requires that you specify both the magnitude (speed) and the <u>direction</u>.  55 ft/sec North, 55 ft/sec horizontally, and 55 ft/sec West at a 45 degree angle to the horizontal, are all very different velocities.\r<BR>\n" );
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document.write( "Having said all that, I suspect that you really meant that the initial velocity is 55 ft/sec <u>up</u>.  So, let's solve the problem using that assumption.\r<BR>\n" );
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document.write( "The acceleration due to the force of gravity on an object near the earth's surface is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ g = -32 \text{ \frac{ft}{sec^2}\">\r<BR>\n" );
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document.write( "Note the minus sign because the accelleration vector is opposite in direction to our velocity vector.\r<BR>\n" );
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document.write( "Integrating with respect to time gives the instantaneous velocity at time <i><b>t</b></i>:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ V(t) = \int\,g\,dt = \int\,-32 \text{ \frac{ft}{sec^2}\,dt = -32t + C \text{ \frac{ft}{sec}}\">\r<BR>\n" );
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document.write( "Where, for this problem, the constant of integration, <i><b>C</b></i>, is the initial velocity, and we will call this <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE v_o\">.  (If the velocity was in a direction other than straight up, then C would be the vertical component of the initial velocity)\r<BR>\n" );
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document.write( "Then integrating the velocity function with respect to time gives the instantaneous height at time <i><b>t</b></i>:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ H(t) = \int\,V(t) = \int\,-32t + v_o \text{ \frac{ft}{sec}} = -16t^2 + v_ot + C \text{ ft}\">\r<BR>\n" );
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document.write( "Where the constant of integration is the initial height which we will call <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE h_o\">.  Hence the final function is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ H(t) = -16t^2 + v_ot + h_o \text{ ft}\">\r<BR>\n" );
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document.write( "And substituting the given initial values:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ H(t) = -16t^2 + 55t + 2 \text{ ft}\">\r<BR>\n" );
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document.write( "Now the problem is to find <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE H(2)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ H(2) = -16(2)^2 + 55(2) + 2 \text{ ft}\">\r<BR>\n" );
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document.write( "The only thing left is a little arithmetic.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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