document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=972110>Question 972110</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help! Sorry it's more than one question<BR>\n" );
document.write( "A ball is thrown straight up with an initial velocity of 40 m/s, so that its height (in meters) after t seconds is: h(t) = 2t(20 &#8722; t).\r<BR>\n" );
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document.write( "(a) Find an expression for the velocity of the ball at time t.\r<BR>\n" );
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document.write( "(b) What is the instantaneous velocity at t = 4? Is the ball rising or falling at this time?\r<BR>\n" );
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document.write( "(c) What is the maximum height achieved by the ball? Hint: the velocity of the ball will be zero when the ball is at its highest point.\r<BR>\n" );
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document.write( "(d) How fast will the ball be travelling when it hits the ground? Hint: first calculate time t when the ball hits the ground. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #594487 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=594487\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> velocity(v) is defined as the first derivative of the position function<BR>\n" );
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document.write( "h(t) = 2t(20 &#8722; t) = 40t - 2t^2<BR>\n" );
document.write( "note that this is a parabola that opens downward<BR>\n" );
document.write( "v = h'(t) = 40 - 4t<BR>\n" );
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document.write( "a) v = h'(t) = 40 - 4t<BR>\n" );
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document.write( "b) v = 40 - (4*4) = 24<BR>\n" );
document.write( "ball is rising<BR>\n" );
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document.write( "c) 0 = 40 - 4t<BR>\n" );
document.write( "-4t = -40<BR>\n" );
document.write( "t = 10 and<BR>\n" );
document.write( "h(10) = 40t - 2t^2<BR>\n" );
document.write( "h(10) = 400 - 200 = 200<BR>\n" );
document.write( "max height is 200 m<BR>\n" );
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document.write( "d) 0 = 40t - 2t^2<BR>\n" );
document.write( "2t^2 = 40t<BR>\n" );
document.write( "t = 20 and<BR>\n" );
document.write( "h'(20) = 40 - 4*20<BR>\n" );
document.write( "h'(20) = -40 which is a downward velocity of 40 m/s\r<BR>\n" );
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