document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1126973>Question 1126973</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, I read this questions and came up with the equation, but I'm not sure if I did it right, can you help me? <BR>\n" );
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document.write( "How far can a soccer player kick a soccer ball down field? Through the application of a linear function and a quadratic function and ignoring wind and air resistance one can describe the path of a soccer ball. These functions depend on two elements that are within the control of the player: velocity of the kick (vk) and angle of the kick (&#952;). A skilled high school soccer player can kick a soccer ball at speeds up to 50 to 60 mi/h, while a veteran professional soccer player can kick the soccer ball up to 80 mi/h. <BR>\n" );
document.write( "*During the game the air and wind resistance play a role in the ball's path, however these factors make the equation more complex.<BR>\n" );
document.write( "*The soccer ball in flight follows a parabolic curve. <BR>\n" );
document.write( " ** so basically it's like a right triangle with \"Vk = Vkick\" on the hypotenuse, \"Vy\" on the opposite side and \"Vx\" on the adjacent side. And a 0 in front of the acute angle between the hypotenuse and the adjacent side.\r<BR>\n" );
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document.write( "Vectors --> The vectors identified in the pattern describe the initial velocity of the soccer ball as the combination of a vertical and horizontal velocity. \r<BR>\n" );
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document.write( "Gravity --> The constant g represents the acceleration of any object due to the Earth's gravitational pull. The value of g near Earth's surface is about -32 ft/s^2. <BR>\n" );
document.write( "   Vx = Vk cos 0 and Vy = Vk sin 0\r<BR>\n" );
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document.write( "1. Use the information above to calculate the horizontal and vertical velocities of a ball kicked at a 35 degree angle with an inital velocity of 60mi/h. Convert the velocities to ft/s. <BR>\n" );
document.write( "      ***so the equation would be 60 = 35 cos -32, which would be 0, so the x value is 0. and then the second equation would be -32 = 60 sin 35 = 34.4 \r<BR>\n" );
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document.write( "2.The equations x(t) = vx t and y(t) = vy t + 0.5 gt^2 describe the x- and y- coordinate of a soccer ball function of time. Use the second to calculate the time the ball will take to complete its parabolic path. \r<BR>\n" );
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document.write( "Do I plug in (0,34.4)? <BR>\n" );
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document.write( "3. Use the first equation given in Question 2 to calculate how far the ball will travel horizontally from its original position. <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #743805 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=743805\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ V_x\ =\ V_k\cos\theta\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ V_y\ =\ V_k\sin\theta\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x(t)\ =\ V_xt\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y(t)\ =\ V_yt\ -\ 16t^2\">\r<BR>\n" );
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document.write( "For your given data\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x(t)\ =\ (60\cos\,35^\circ)t\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y(t)\ =\ (60\sin\,35^\circ)t\ -\ 16t^2\">\r<BR>\n" );
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document.write( "Remember, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y(t)\"> is positive when the ball is in the air, but gravity is pulling it down, hence the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE -\ 16t^2\"> acceleration due to gravity.\r<BR>\n" );
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document.write( "The ball will be at zero feet above the ground, i.e., <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y(t)\ =\ 0\"> at two times: one at <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large t\ =\ 0\">, the instant that the ball is kicked, and the other when it has completed its path.\r<BR>\n" );
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document.write( "Solve\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y(t)\ =\ 0\">\r<BR>\n" );
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document.write( "and select the non-zero root as the answer to question 2, and then evaluate <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x(t)\"> for that value of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE t\"> to get the answer to question 3.<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" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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