document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=35899>Question 35899</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose you throw a baseball straight up at a velocity of 32 feet per second. A function can be created by expressing distance above the ground, s, as a function of time, t. This function is s = -16t2 + v0t + s0 <BR>\n" );
document.write( "•	16 represents ½g, the gravitational pull due to gravity (measured in feet per second 2). <BR>\n" );
document.write( "•	v0 is the initial velocity (how hard do you throw the object, measured in feet per second).<BR>\n" );
document.write( "•	s0 is the initial distance above ground (in feet). If you are standing on the ground, then s0 = 0.<BR>\n" );
document.write( "      a)What is the function that describes this problem?<BR>\n" );
document.write( "      b)The ball will be how high above the ground after 1 second?<BR>\n" );
document.write( "      c)How long will it take to hit the ground?<BR>\n" );
document.write( "      d)What is the maximum height of the ball? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #22397 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=22397\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> LET ME SHOW YOU THE WORKING OF YOUR<BR>\n" );
document.write( "SPECIFIC PROBLEM<BR>\n" );
document.write( "3) Suppose you throw a baseball straight up at a<BR>\n" );
document.write( "velocity of 32 feet per second. A function can be<BR>\n" );
document.write( "created by expressing distance above the ground, s, as<BR>\n" );
document.write( "a function of time, t. This function is s = -16t2 +<BR>\n" );
document.write( "v0t + s0<BR>\n" );
document.write( "&#65533; 16 represents &#65533;g, the gravitational pull due to<BR>\n" );
document.write( "gravity (measured in feet per second 2).<BR>\n" );
document.write( "&#65533; v0 is the initial velocity (how hard do you throw<BR>\n" );
document.write( "the object, measured in feet per second).<BR>\n" );
document.write( "&#65533; s0 is the initial distance above ground (in feet).<BR>\n" );
document.write( "If you are standing on the ground, then s0 = 0.<BR>\n" );
document.write( "a) What is the function that describes this problem?<BR>\n" );
document.write( "Answer:<BR>\n" );
document.write( "THIS IS WHAT IS GIVEN ABOVE<BR>\n" );
document.write( "S=-16*T^2+V0*T+S0<BR>\n" );
document.write( ".....................................I<BR>\n" );
document.write( "WITH THE ELABORATIONS GIVEN ABOVE.<BR>\n" );
document.write( "b) The ball will be how high above the ground after 1<BR>\n" );
document.write( "second?<BR>\n" );
document.write( "Answer:<BR>\n" );
document.write( "Show work in this space.<BR>\n" );
document.write( "WE ARE GIVEN<BR>\n" );
document.write( "V0=32 FPS<BR>\n" );
document.write( "S0=0...BALL THROWN FROM GROUND AND DISTANCE MEASURED<BR>\n" );
document.write( "FROM GROUND<BR>\n" );
document.write( "T=1 SEC...<BR>\n" );
document.write( "S=?<BR>\n" );
document.write( "HENCE SUBSTITUTING IN EQN.I,WE GET<BR>\n" );
document.write( "S=-16*1^2+32*1+0=-16+32=16 FT.<BR>\n" );
document.write( "c) How long will it take to hit the ground?<BR>\n" );
document.write( "Answer:<BR>\n" );
document.write( "Show work in this space.<BR>\n" );
document.write( "WE ARE GIVEN HERE<BR>\n" );
document.write( "V0=32<BR>\n" );
document.write( "S0=0<BR>\n" );
document.write( "S=0<BR>\n" );
document.write( "T=?<BR>\n" );
document.write( "HENCE SUBSTITUTING IN EQN.I,WE GET<BR>\n" );
document.write( "0=-16T^2+32T+0<BR>\n" );
document.write( "16T(-T+2)=0<BR>\n" );
document.write( "T=0...OR....-T+2=0....OR....T=2 SEC.<BR>\n" );
document.write( "SINCE T=0 REPRESENTS THE INTIAL POSITION<BR>\n" );
document.write( "T=2 SEC.IS THE ANSWER WHEN IT HITS THE GROUND AGAIN<BR>\n" );
document.write( "AFTER GOING UP AND FALLING DOWN.<BR>\n" );
document.write( "d) What is the maximum height of the ball?<BR>\n" );
document.write( "Answer:<BR>\n" );
document.write( "Show work in this space.<BR>\n" );
document.write( "HERE WE ARE GIVEN<BR>\n" );
document.write( "V0=32<BR>\n" );
document.write( "S0=0....AND THERE ARE 2 ASPECTS TO TAKE NOTE OF.<BR>\n" );
document.write( "1.THE BALL GOES UP FIRST SLOWING DOWN AS IT GOES UP<BR>\n" );
document.write( "DUE TO EARTHS GRAVITATION...NOTE -16 GRAVITATIONAL<BR>\n" );
document.write( "ACCELERATIONED MENTIONED IN THE PROBLEM. IT GOES UP<BR>\n" );
document.write( "TILL ITS VELOCITY BECOMES ZERO FROM THE INITIAL<BR>\n" );
document.write( "VELOCITY OF THROW OF 32 FPS.AND THEN FALLS DOWN<BR>\n" );
document.write( "REGAINING THE SAME VELOCITY WHEN IT HITS THE GROUND AS<BR>\n" );
document.write( "PER PHYSICS LAWS,NEGLECTING AIR DRAG.<BR>\n" );
document.write( "2.IT IS ALSO PROVED IN PHYSICS IN SUCH CASES,THAT<BR>\n" );
document.write( "i)THE TIME OF ASCENT = THE TIME OF DESCENT<BR>\n" );
document.write( "ii)THE DISTANCE TRAVELLED UPWARD=THE DISTANCE TRVELLED<BR>\n" );
document.write( "DOWN WARD<BR>\n" );
document.write( "iii)THE VELOCITY WITH WHICH IT IS THROWN UP= THE<BR>\n" );
document.write( "VELOCITY WITH WHICH IT HITS THE GROUND.<BR>\n" );
document.write( "HENCE USING i)PRINCIPLE ,SINCE TOTAL TIME OF TRAVEL AS<BR>\n" );
document.write( "PER C) AS WE ALCULATED IS 2 SEC.,TIME OF ASCENT =1<BR>\n" );
document.write( "SEC.HENCE MAXIMUM HEIGHT REACHED IS DISTANCE TRAVELLED<BR>\n" );
document.write( "IN 1 SEC=16 FT.AS SHOWN IN B).<BR>\n" );
document.write( "---------<BR>\n" );
document.write( "ANOTHER METHOD IS TO FIND WHEN THE VELOCITY WILL<BR>\n" );
document.write( "BECOME ZERO AS IT GOES UP AND FIND THE DISTANCE<BR>\n" );
document.write( "TRAVELLED IN THAT TIME.<BR>\n" );
document.write( "THE FORMULA FOR THAT IS OBTAINED BY DIFFERENTIATING<BR>\n" );
document.write( "THE GIVEN EQN.II<BR>\n" );
document.write( "AS FOLLOWS<BR>\n" );
document.write( "DS/DT=VELOCITY=V=-32*T+V0...WHERE V IS THE FINAL<BR>\n" );
document.write( "VELOCITY AFTER T SECS.<BR>\n" );
document.write( "SINCE AT MAXMUM HEIGHT FINAL VELOCITY =0 (AS THEN ONLY<BR>\n" );
document.write( "IT FALLS BACK TOWARDS GROUND.)<BR>\n" );
document.write( "HENCE 0=-32T+32<BR>\n" );
document.write( "32T=32<BR>\n" );
document.write( "T=1...AS WE USED EARLIER NOW WE FIND S=16 FT.AS<BR>\n" );
document.write( "BEFORE.<BR>\n" );
document.write( "HOPE YOU UNDERSTOOD. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );