document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1047598>Question 1047598</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An arrow is shot straight up in the air with an initial speed of 220 ft/s. If on striking the ground it embeds itself 2.00 in into the ground, find the magnitude of the acceleration (assumed constant) required to stop the arrow, in units of feet/second^2. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #663131 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=663131\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The arrow is fired 220 ft/s straight up, reaches a maximum height, then falls straight down. The final velocity when it reaches the ground is then used to find the acceleration needed to go from that velocity to zero, over a distance of 2.00 inches, or 2/12 = 1/6 ft. <BR>\n" );
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document.write( "since the arrow is fired straight up, the y component is  sin(90) * 220 = 220<BR>\n" );
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document.write( "when the arrow reaches max height its velocity is 0, therefore<BR>\n" );
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document.write( "0 = 220 + (-32t) <BR>\n" );
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document.write( "note that 32 is acceleration of gravity acting downward on the arrow<BR>\n" );
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document.write( "t = 220 / 32 = 6.975 seconds<BR>\n" );
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document.write( "max height of arrow = 220 * 6.975 = 1512.5 feet<BR>\n" );
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document.write( "at max height the arrow has potential energy that equals its kinetic energy at ground 0<BR>\n" );
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document.write( "mgh = (1/2)mv^2<BR>\n" );
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document.write( "32(1512.5) = (1/2)v^2<BR>\n" );
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document.write( "v^2 = 96800<BR>\n" );
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document.write( "v = 311.1 ft/sec<BR>\n" );
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document.write( "now use the equation<BR>\n" );
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document.write( "v(f)^2 = v(0)^2 + 2as<BR>\n" );
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document.write( "0 = 311.1^2 + 2a(1/6)<BR>\n" );
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document.write( "(1/3)*(a) = -96800<BR>\n" );
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document.write( "a = -290400<BR>\n" );
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document.write( "magnitude of acceleration to stop arrow is 290400 ft/sec^2<BR>\n" );
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document.write( " </SPAN>\n" );
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