document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1170979>Question 1170979</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A ball is thrown off a 30 m cliff at 20 m/s at an angle of 60 degrees above the horizontal<BR>\n" );
document.write( "What is the maximum height of the object? <BR>\n" );
document.write( "What is the total hang time of the ball?<BR>\n" );
document.write( "What is the final velocity of the ball?<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 #795857 by </B><A HREF=/tutors/aboutme.mpl?userid=htmentor><B>htmentor(1343)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=htmentor><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=htmentor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=795857\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The total height will be h0 + h, where h0 is the height of the cliff<BR>\n" );
document.write( "We can use the formula v2^2 = v1^2 + 2ah, with v1 = vy = 20*sin(60), and a = g<BR>\n" );
document.write( "h = vy^2/2g<BR>\n" );
document.write( "I assume total hang time refers to the time the ball takes to hit the ground.<BR>\n" );
document.write( "The time to reach maximum height is determined from v2 = v1 + at, <BR>\n" );
document.write( "with v2 = 0. Thus t = vy/g<BR>\n" );
document.write( "The time to fall from the maximum height to the ground is determined from<BR>\n" );
document.write( "h + h0 = v1t + 1/2at^2.  Since v1 = 0, we have t = sqrt(2(h + h0)/g)<BR>\n" );
document.write( "Now for the final velocity, we need to determine the x and y components<BR>\n" );
document.write( "vx will remain constant throughout, and is equal to 20*cos(60)<BR>\n" );
document.write( "The y component of the final velocity is obtained from v2^2 = v1^2 + 2a(h+h0)<BR>\n" );
document.write( "with v1 = 0<BR>\n" );
document.write( "I will leave it to you to fill in the values and get the final numbers<BR>\n" );
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