document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1207029>Question 1207029</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Example on free fall:\r<BR>\n" );
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document.write( "1. A body is released from rest and falls freely. Compute its position and velocity after 1 and 2s. Take the origin at the elevation of the starting point, the y-axis vertical, and the upward direction as positive.\r<BR>\n" );
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document.write( "2. A stone is thrown from the top of a building with an initial velocity of 20 m/s straight upward. The building is 50 m high, and the stone just misses the edge of the roof on its way down. Determine:\r<BR>\n" );
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document.write( "(a) the time needed for the stone to reach its maximum height,\r<BR>\n" );
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document.write( "(b) the maximum height,\r<BR>\n" );
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document.write( "(c) the time needed for the stone to return to the level of thrower,\r<BR>\n" );
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document.write( "(d) the velocity of the stone at this instant, and\r<BR>\n" );
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document.write( "(e) the velocity and the position of the stone at t =5s.\r<BR>\n" );
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document.write( "(f) the velocity of the stone just before it hits the ground\r<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 #844883 by </B><A HREF=/tutors/aboutme.mpl?userid=mananth><B>mananth(16946)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mananth><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=mananth><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=844883\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "1. A body is released from rest and falls freely. Compute its position and velocity after 1 and 2s. Take the origin at the elevation of the starting point, the y-axis vertical, and the upward direction as positive.\r<BR>\n" );
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document.write( "An object that is moving under only the influence of gravity is in free fall<BR>\n" );
document.write( "Acceleration due to gravity is generally taken as 9.8 m/s^2\r<BR>\n" );
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document.write( "We use newton's equation of motion <BR>\n" );
document.write( "v=u+at<BR>\n" );
document.write( "v = final velocity <BR>\n" );
document.write( " u initial velocity, a =Acceleration due to gravity, t = time in seconds\r<BR>\n" );
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document.write( "The object falls from rest so u=0 a= g = -9.8 m/s^2, t = 1 (s)<BR>\n" );
document.write( "v= 0+(-9.8)(1) = -9.8 m/s \r<BR>\n" );
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document.write( "Distance = average velocity * time = (0+(-9.8))/2 *1= -4.9 *1 = -4.9 m  (After 1 second)\r<BR>\n" );
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document.write( "Similarly find for 2 seconds  here t=2\r<BR>\n" );
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document.write( "2. A stone is thrown from the top of a building with an initial velocity of 20 m/s straight upward. The building is 50 m high, and the stone just misses the edge of the roof on its way down. Determine:<BR>\n" );
document.write( "(a) the time needed for the stone to reach its maximum height,\r<BR>\n" );
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document.write( "Newton's First law of motion<BR>\n" );
document.write( "v= u+at<BR>\n" );
document.write( "0= 20+(-9.8) *t  (The object reaches maximum height) v=0\r<BR>\n" );
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document.write( "-20/-9.8 = t<BR>\n" );
document.write( "t = 2.04 s\r<BR>\n" );
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document.write( "(b) the maximum height,<BR>\n" );
document.write( "Newton.s second law of motion<BR>\n" );
document.write( "s= ut+1/2 g t^2   ( here a=g)\r<BR>\n" );
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document.write( "s = 20*(2.04) + 1/2 * (-9.8)*(2.04)^2<BR>\n" );
document.write( "s= 20.40 m\r<BR>\n" );
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document.write( "(c) the time needed for the stone to return to the level of thrower,\r<BR>\n" );
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document.write( "time to go up = time to come down \r<BR>\n" );
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document.write( "2*2.04 = 4.08 s\r<BR>\n" );
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document.write( "(d) the velocity of the stone at this instant, and<BR>\n" );
document.write( "The object is falling under gravitational force only\r<BR>\n" );
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document.write( "t = 2.04 s ,g= -9.8 m/s^2<BR>\n" );
document.write( "v= 0+2.04*(-9.8)<BR>\n" );
document.write( "v = -19.992 m/s\r<BR>\n" );
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document.write( "(e) the velocity and the position of the stone at t =5s.\r<BR>\n" );
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document.write( "Again v= u+at<BR>\n" );
document.write( "v = 0+(-9.8)*5<BR>\n" );
document.write( "v = -49m/s\r<BR>\n" );
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document.write( "Position <BR>\n" );
document.write( "v^2= u^2 +2gs\r<BR>\n" );
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document.write( "-49^2= 0^2+ 2*(-9.8)*s     ( s is distance)\r<BR>\n" );
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document.write( "(-49)^2/(2*(-9.8) )= s <BR>\n" );
document.write( "s= -122.5 m\r<BR>\n" );
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document.write( "(f) the velocity when it touches the ground<BR>\n" );
document.write( "The height  from which  it is falling is 50 (height of building)+20.40( maximum height reached) = 70.40 m \r<BR>\n" );
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document.write( "v^2= u^2+2gs ( Newton's Third law of motion)\r<BR>\n" );
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document.write( "v^2 = 0+2*(-9.8)*70.40\r<BR>\n" );
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document.write( "v= sqrt(2*(-9.8)*70.40)\r<BR>\n" );
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document.write( "v = -37.15 m/s\r<BR>\n" );
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document.write( "The negative signs indicate  downward direction \r<BR>\n" );
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