document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=890666>Question 890666</A>: <I><SPAN STYLE=\"word-break: break-all;\"> When a basketball player shoots a ball from his hand at an initial of 2 m with an initial upward velocity of 10 meters per second, the height of the ball can be modeled by the quadratic expression -4.9t^2 + 10t + 2 after t seconds.<BR>\n" );
document.write( "a. What will be the height of the ball after 2 seconds?<BR>\n" );
document.write( "b. How long will it take the ball to reach the height of 4.5 m?<BR>\n" );
document.write( "  How long will it take to touch the ground?<BR>\n" );
document.write( "c. Do you think the ball will reach the height of 12 m? Why?<BR>\n" );
document.write( "d. Will the ball hit the ring if the ring is 3 m high?<BR>\n" );
document.write( "e. Write a similar situation with varied initial height when the ball is thrown with an initial upward velocity. Then model the path of the ball by quadratic expression.<BR>\n" );
document.write( "f. Using the equation and the quadratic expression you have written in item e, formulate and solve problems involving the height of the ball when it is thrown after a given time.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #539140 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=539140\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> When a basketball player shoots a ball from his hand at an initial of 2 m with an initial upward velocity of 10 meters per second, the height of the ball can be modeled by the quadratic expression -4.9t^2 + 10t + 2 after t seconds.<BR>\n" );
document.write( "a. What will be the height of the ball after 2 seconds?<BR>\n" );
document.write( "h(t) = -4.9t^2 + 10t + 2<BR>\n" );
document.write( "Sub 2 for t<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "b. How long will it take the ball to reach the height of 4.5 m?<BR>\n" );
document.write( "h(t) = -4.9t^2 + 10t + 2 = 4.5<BR>\n" );
document.write( "Solve for t<BR>\n" );
document.write( "---<BR>\n" );
document.write( "  How long will it take to touch the ground?<BR>\n" );
document.write( "h(t) = -4.9t^2 + 10t + 2 = 0<BR>\n" );
document.write( "Solve for t<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "c. Do you think the ball will reach the height of 12 m?<BR>\n" );
document.write( "The max height is the vertex of the parabola.<BR>\n" );
document.write( "The vertex is on the axis of symmetry, t = -b/2a = -10/-9.8<BR>\n" );
document.write( "Max ht is at 50/49 seconds<BR>\n" );
document.write( "h(t) = -4.9t^2 + 10t + 2<BR>\n" );
document.write( "Sub (50/49) for t for max ht.<BR>\n" );
document.write( "-----------<BR>\n" );
document.write( " Why?<BR>\n" );
document.write( "d. Will the ball hit the ring if the ring is 3 m high?<BR>\n" );
document.write( "Depends on the max ht above.<BR>\n" );
document.write( "h(t) give the height of the center of the ball, take that into account.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "e. Write a similar situation with varied initial height when the ball is thrown with an initial upward velocity. Then model the path of the ball by quadratic expression.<BR>\n" );
document.write( "h(t) = -4.9t^2 + 10t + ho (ho = initial height)<BR>\n" );
document.write( "------<BR>\n" );
document.write( "f. Using the equation and the quadratic expression you have written in item e, formulate and solve problems involving the height of the ball when it is thrown after a given time.<BR>\n" );
document.write( "Same as above </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );