document.write( "Question 141576This question is from textbook nelson mathematics 10
\n" ); document.write( ": A model rocket is shot straight up from the roof of a school. The height at any time t is approximated by the model H = 15 + 23t -5t squared, where H is the height in metres and t is the time in seconds.
\n" ); document.write( "a) How long does it take for the rocket to pass a window 10 m above the ground?
\n" ); document.write( "b) When does the rocket hit the ground?
\n" ); document.write( "c)What is the max height the rocket reaches above the roof of the school? \n" ); document.write( "
Algebra.Com's Answer #103249 by ankor@dixie-net.com(22740)\"\" \"About 
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A model rocket is shot straight up from the roof of a school. The height at any time t is approximated by the model H = 15 + 23t -5t squared, where H is the height in metres and t is the time in seconds.
\n" ); document.write( ":
\n" ); document.write( "Write the equation in the standard form:
\n" ); document.write( "h = -5t^2 + 23t + 15
\n" ); document.write( ":
\n" ); document.write( "you should recognize the 3 parts of this equation
\n" ); document.write( "-5x^2 is the force of gravity in m/sec, hence it is negative
\n" ); document.write( "23x is the upward velocity of the rocket in m/sec, hence it is positive
\n" ); document.write( "15 is the initial height or in this case the height of the school
\n" ); document.write( ":
\n" ); document.write( "a) How long does it take for the rocket to pass a window 10 m above the ground?
\n" ); document.write( "h = 10
\n" ); document.write( "-5t^2 + 23t + 15 = 10
\n" ); document.write( "-5t^2 + 23t + 15 - 10 = 0
\n" ); document.write( "-5t^2 + 23t + 5 = 0
\n" ); document.write( "Solve for t using the quadratic formula:
\n" ); document.write( "\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"
\n" ); document.write( "In this equation a=-5; b=23; c=5
\n" ); document.write( "\"t+=+%28-23+%2B-+sqrt%2823%5E2+-+4+%2A+-5+%2A+5+%29%29%2F%282%2A-5%29+\"
\n" ); document.write( "\"t+=+%28-23+%2B-+sqrt%28529+-+%28-100%29+%29%29%2F%28-10%29+\"
\n" ); document.write( "\"t+=+%28-23+%2B-+sqrt%28529+%2B+100+%29%29%2F%28-10%29+\"
\n" ); document.write( "\"t+=+%28-23+%2B-+sqrt%28629%29%29%2F%28-10%29+\"
\n" ); document.write( "Two solutions, but we only want the positive one:
\n" ); document.write( "\"t+=+%28-23+-+25.08%29%2F%28-10%29\"
\n" ); document.write( "t = \"%28-48.08%29%2F%28-10%29\"
\n" ); document.write( "t = + 4.8 sec the rocket will pass a window 10' from the ground
\n" ); document.write( ":\r
\n" ); document.write( "\n" ); document.write( "b) When does the rocket hit the ground?
\n" ); document.write( "The rocket hits the ground when h = 0, so we have:
\n" ); document.write( "-5t^2 + 23t + 15 = 0
\n" ); document.write( "Solve this equation using the quadratic formula just like we did above, except c = 15
\n" ); document.write( "You should get t ~ 5.18 sec
\n" ); document.write( ":
\n" ); document.write( "c)What is the max height the rocket reaches above the roof of the school?
\n" ); document.write( "The max height will occur at the axis of symmetry, find that using t=-b/(2a)
\n" ); document.write( "In this problem remember a=-5; b=23
\n" ); document.write( "t = \"%28-23%29%2F%282%2A-5%29\"
\n" ); document.write( "t = \"%28-23%29%2F%28-10%29\"
\n" ); document.write( "t = + 2.3 sec with me max height
\n" ); document.write( ";
\n" ); document.write( "Find the max height, substitute 2.3 for t in the equation and find h
\n" ); document.write( "h = -5(2.3^2) + 23(2.3) + 15
\n" ); document.write( "h = -5(5.29) + 52.9 + 15
\n" ); document.write( "h = -26.45 + 52.9 + 15
\n" ); document.write( "h = 41.45 m is the max height
\n" ); document.write( ":
\n" ); document.write( "A graph illustrates all this
\n" ); document.write( "\"+graph%28+300%2C+200%2C+-4%2C+6%2C+-10%2C+50%2C+-5x%5E2%2B23x%2B15%29+\"
\n" ); document.write( ";
\n" ); document.write( "did all this make sense to you? any questions? \n" ); document.write( "
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