document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=947649>Question 947649</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A projectile is fired from a cliff 200 above the water at an inclination of 45 degree to the horizontal, with a muzzle velocity of 50 feet per second. the height is given by h(x)= -32x^2/(50)^2+x+200<BR>\n" );
document.write( "a. at what horizontal distance from the face of the cliff will the projectile strike the water? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #578338 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=578338\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> we are given <BR>\n" );
document.write( "h(x)= -32x^2/(50)^2+x+200, where x is time<BR>\n" );
document.write( "let x1 be the axis of symmetry of this parabola that curves downward<BR>\n" );
document.write( "x1 = -b/2a = (-1/2*(-32/50^2)) = 39.0625 seconds<BR>\n" );
document.write( "now substitute in h(39.0625)<BR>\n" );
document.write( "h(39.0625) = ((-32*(39.0625^2))/50^2)+39.0625+200 = 219.53125 feet max height<BR>\n" );
document.write( "now the height of the cliff is 200 feet so 219.53125 - 200 = 19.53125 feet above cliff and remember that the projectile is launched at 45 degrees, therefore the horizontal distance to the max height is calculated<BR>\n" );
document.write( "tan(45 degrees) = 19.53125 / d and<BR>\n" );
document.write( "d = 19.53125 / tan(45 degrees) = 19.53125 / 1 = 19.53125 feet<BR>\n" );
document.write( "d is the horizontal distance to the max height of the projectile, we have the following ratio<BR>\n" );
document.write( "(39.0625 / 19.53125) = (170.023864174 / x2) where x2 is the horizontal distance to where the projectile strikes the water and 170.023864174 is the number of seconds when the projectile strikes the water (calculated by solving 0 = -32x^2/(50)^2+x+200)<BR>\n" );
document.write( "x2 = (19.53125 * 170.023864174) / 39.0625 =  85.011932087 feet<BR>\n" );
document.write( "The distance from the cliff to where the projectile strikes the water is 85.011932087 feet\r<BR>\n" );
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