document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=202884>Question 202884</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Could one of the Calculus tutors please help me with the following Advanced Calculus question. PLEASEE!!!!\r<BR>\n" );
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document.write( "A stunt diver leaps off a bridge 50m above a river with an initial upward velocity of 10m/s. Her altitude is given by h= (-5t^2+10t+50, where t is in seconds and h is in metres.<BR>\n" );
document.write( "a)Construct a table of values to illustrate her height in 1-second intervals until she hits the water.(2 marks)<BR>\n" );
document.write( "b)What does a negative value for height represent?(1 mark)<BR>\n" );
document.write( "c)Construct a table showing her velocity during 1-second intervals starting at time 0.(2 marks)<BR>\n" );
document.write( "d)When does her velocity change from positive to negative?(1 mark)<BR>\n" );
document.write( "e)What does this change represent?(1 mark)<BR>\n" );
document.write( "f)When does she hit the water?(1 mark)<BR>\n" );
document.write( "g)What is her average velocity in the half-second before she hits the river?(1 mark)<BR>\n" );
document.write( "h)Why is her average velocity from t=0 to t=2 equal to 0?(1 mark) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #153047 by </B><A HREF=/tutors/aboutme.mpl?userid=dyakobovitch><B>dyakobovitch(40)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=dyakobovitch><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=153047\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A stunt diver leaps off a bridge 50m above a river with an initial upward velocity of 10m/s. Her altitude is given by h= (-5t^2+10t+50, where t is in seconds and h is in metres.\r<BR>\n" );
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document.write( "a)Construct a table of values to illustrate her height in 1-second intervals <BR>\n" );
document.write( "until she hits the water.(2 marks)\r<BR>\n" );
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document.write( "We assume that the time function starts at t=0. So, we choose (h,t)= (0,50) (1,55), (2,50) (3,35) (4,10)...\r<BR>\n" );
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document.write( "The function reduces to -5(t^2-2t-10) =0, and so you hit the water at time= 1 + sqrt(11) seconds (by solving the quadratic formula).\r<BR>\n" );
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document.write( "b)What does a negative value for height represent?(1 mark)\r<BR>\n" );
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document.write( "A negative value for height means that you are under water in the river. =)\r<BR>\n" );
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document.write( "c)Construct a table showing her velocity during 1-second intervals starting at time 0.(2 marks)\r<BR>\n" );
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document.write( "To find the velocity, you need to take the derivative of the height function. so h'(t)=-10t+10. Inserting the time values from above, we have our velocity as (0,10), (1,0), (2,-10), (3,-20), (4,-30), etc... Notice how the velocity becomes negative. This indicates that we are taking a downward trajectory and are accelerating downward from gravity.\r<BR>\n" );
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document.write( "d)When does her velocity change from positive to negative?(1 mark)\r<BR>\n" );
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document.write( "This is the critical value for the h'(t), which occurs at t=1 or when h'(t)=0.\r<BR>\n" );
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document.write( "e)What does this change represent?(1 mark)\r<BR>\n" );
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document.write( "That our concavity is changing, we are now accelerating downward, that we have negative velocity, that we have reached our maximum height and are now falling. (When you jump off a bridge you first increase in height ever-so-slightly, before reaching that maximum height and then falling as you dive downward.\r<BR>\n" );
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document.write( "f)When does she hit the water?(1 mark)\r<BR>\n" );
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document.write( "Review part a) at time= 1 + sqrt(11) seconds.\r<BR>\n" );
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document.write( "g)What is her average velocity in the half-second before she hits the river?(1 mark)\r<BR>\n" );
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document.write( "Since she hits the water at 1 + sqrt(11) seconds, I assume you are looking for the specific velocity at the half second before, not the average velocity. Therefore, using the time input of 0.5 + sqrt(11) seconds in the h'(t) function, we get her velocity as -10(0.5 + sqrt(11)) + 10 = 5 -10sqrt(11) as her velocity. Notice this is a check for the problem since the velocity is negative, indicating that she is moving downward.\r<BR>\n" );
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document.write( "h)Why is her average velocity from t=0 to t=2 equal to 0?(1 mark)\r<BR>\n" );
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document.write( "Average velocity is the sum of velocity divided by the time interval. Her velocity at t=2 is -10. Her velocity at 0=10. So average velocity is (-10 + 10)/2=0.\r<BR>\n" );
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document.write( "Feel free to comment if you have any more questions or concerns. - David </SPAN>\n" );
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