document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1163928>Question 1163928</A>: <I><SPAN STYLE=\"word-break: break-all;\"> At a baseball game, the batter hits the baseball straight up at an initial velocity of +42m/s.<BR>\n" );
document.write( " A) at what time will the ball reach its highest point<BR>\n" );
document.write( "b) what will be the maximum height the ball reaches\r<BR>\n" );
document.write( "\n" );
document.write( "BTW the answer is about 4.3 secs for part a and 90 m for part b.. could you pls show me the steps i need its for my hw. THANKS!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #788182 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=788182\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Using the mks measurement system, the function that describes the height of a projectile where the gravitational acceleration constant is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large g\"> at time <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large t\"> with an initial vertical velocity component magnitude of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large v_o\"> and an initial height of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large h_o\"> is:\r<BR>\n" );
document.write( "\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ h(t)\ =\ \frac{1}{2}gt^2\ +\ v_ot\ +\ h_o\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "For objects near the earth's surface, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large g\ =\ -9.8\text{ m/sec^2}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Since you don't specify the height of the ball when the bat impacted it, we have to assume <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large h_o\ =\ 0\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "That makes your function:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ h(t)\ =\ -4.9t^2\ +\ 42t\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This would graph as a concave down parabola because the lead coefficient is negative.  The answer to part a) is the value of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large t\"> at the vertex of the parabola.  The answer to part b) is the value of the function at the answer to part a.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If you have a parabola described by:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \rho(t)\ =\ at^2\ +\ bt\ +\ c\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large t\">-coordinate of the vertex is given by <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large -\frac{b}{2a}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The value of the function at the vertex is then:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \rho\(-\frac{b}{2a}\)\ =\ a\(-\frac{b}{2a}\)^2\ +\ b\(-\frac{b}{2a}\)\ +\ c\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "4.3 seconds is close enough for part a, but part b is inaccurate by an amount equal to the actual height of the ball when the bat hit it.  The bat certainly wasn't on the ground if the batter hit a pop-up.  So, that bat had to be a meter to a meter and a half off of the ground -- perhaps more, and the real world answer to part b would be somewhere in the range of 91 to 92 meters.\r<BR>\n" );
document.write( "\n" );
document.write( "																<BR>\n" );
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" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src=\"http://c0rk.blogs.com/gr0undzer0/darwin-fish.jpg\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );