document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1194321>Question 1194321</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The soccer player kicks the ball in the Figure above with an initial velocity of 35 m/s at an angle of 20°. (a) Calculate for the time when it reaches 0.40 m. (b) Find its position parallel to the field at height equal to 0.40 m. (c) Find the time when it reaches its highest point. (d) At what point is the ball at its highest and farthest? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #826507 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=826507\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The soccer player kicks the ball in the Figure above with an initial velocity of 35 m/s at an angle of 20°. (a) Calculate for the time when it reaches 0.40 m. (b) Find its position parallel to the field at height equal to 0.40 m. (c) Find the time when it reaches its highest point. (d) At what point is the ball at its highest and farthest?<BR>\n" );
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document.write( "Neglecting air friction and using 9.8m/sec/sec for gravity:<BR>\n" );
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document.write( "(a) Calculate for the time when it reaches 0.40 m.<BR>\n" );
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document.write( "The vertical component is 35*sin(20) m/sec.<BR>\n" );
document.write( "Height h(t) = -4.9t^2 + 35*sin(20)*t = 0.4<BR>\n" );
document.write( "4.9t^2 - 35*sin(20)t = -0.4<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4.9t%5E2+-+35%2Asin%2820%29t+%2B+0.4+=+0 ALIGN=MIDDLE  ALT=\"4.9t%5E2+-+35%2Asin%2820%29t+%2B+0.4+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solve the quadratic for t.  There are 2 values, ascending then descending.<BR>\n" );
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document.write( "(b) Find its position parallel to the field at height equal to 0.40 m.<BR>\n" );
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document.write( "If that means its distance from where it was kicked:<BR>\n" );
document.write( "The horizontal component is 35*cos(20)*t<BR>\n" );
document.write( "Calculate using the t values from (a).<BR>\n" );
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document.write( "(c) Find the time when it reaches its highest point.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29+=+-4.9t%5E2+%2B+35%2Asin%2820%29t+-+0.4 ALIGN=MIDDLE  ALT=\"h%28t%29+=+-4.9t%5E2+%2B+35%2Asin%2820%29t+-+0.4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "It's a parabola.  The max is at t = -b/2a = 35*sin(20)/9.8<BR>\n" );
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document.write( "(d) At what point is the ball at its highest<BR>\n" );
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document.write( "At t = the value in (c)<BR>\n" );
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document.write( " and farthest?<BR>\n" );
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document.write( "Multiply t from (c) times 2 times the horizontal component. </SPAN>\n" );
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