document.write( "Question 396170: A toy rocket is launched from a platform that is 4 feet above the ground. The height, h, in feet, of the rocket t seconds after launch is given by h= -16t^2 + 160t + 4. How many seconds after launch will the rocket be 100 feet above the ground? \n" ); document.write( "

Algebra.Com's Answer #281106 by CharlesG2(834) $\"\"$ $\"About$

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A toy rocket is launched from a platform that is 4 feet above the ground. The height, h, in feet, of the rocket t seconds after launch is given by h= -16t^2 + 160t + 4. How many seconds after launch will the rocket be 100 feet above the ground? \r
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\n" ); document.write( "\n" ); document.write( "h = -16t^2 + 160t + 4
\n" ); document.write( "plug in 100 feet for h and solve for t
\n" ); document.write( "100 = -16t^2 + 160t + 4
\n" ); document.write( "(100/-16) = t^2 - 10t - 1/4
\n" ); document.write( "-25/4 = t^2 - 10t - 1/4
\n" ); document.write( "0 = t^2 - 10t + 24/4
\n" ); document.write( "0 = t^2 - 10t + 6
\n" ); document.write( "use quadratic formula with a=1, b=-10, c=6:
\n" ); document.write( " $\"t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"$
\n" ); document.write( " $\"t+=+%2810+%2B-+sqrt%28+100+-+4%2A6+%29%29%2F2+\"$
\n" ); document.write( " $\"t+=+%2810+%2B-+sqrt%28+100+-+24+%29%29%2F2+\"$
\n" ); document.write( " $\"t+=+%2810+%2B-+sqrt%28+76+%29%29%2F2+\"$
\n" ); document.write( "t = 5 +- sqrt(76)/2
\n" ); document.write( "t = 5 +- 2sqrt(19)/2
\n" ); document.write( "t = 5 +- sqrt(19)
\n" ); document.write( "t = 0.641101 rounded to 6 decimal places seconds
\n" ); document.write( "or t = 9.358899 rounded to 6 decimal places seconds
\n" ); document.write( "check:
\n" ); document.write( "100 = -16t^2 + 160t + 4
\n" ); document.write( "100 = -16(0.641101)^2 + 160(0.641101) + 4
\n" ); document.write( "100 = -6.576167875216 + 102.57616 + 4
\n" ); document.write( "100 = 100, yes
\n" ); document.write( "100 = -16(9.358899)^2 + 160(9.358899) + 4
\n" ); document.write( "100 = -1401.423847875216 + 1497.42384 + 4
\n" ); document.write( "100 = 100, yes
\n" ); document.write( "what is highest point and when?
\n" ); document.write( "use vertex form y = a(x-h)^2+k, where h,k is vertex
\n" ); document.write( "h = -16t^2 + 160t + 4, in this case h is y, and t is x
\n" ); document.write( "h = -16(t^2 - 10t) + 4
\n" ); document.write( "h = -16(t^2 - 10t + 25) + 4 + 400 (-16 * 25 = - 400)
\n" ); document.write( "h = -16(t - 5)^2 + 404, vertex is (5,404)
\n" ); document.write( "check with t=5 seconds:
\n" ); document.write( "h = -16(5)^2 + 160(5) + 4
\n" ); document.write( "h = -16 * 25 + 800 + 4
\n" ); document.write( "h = -400 + 800 + 4 = 400 + 4 = 404, yes and highest point is 404 feet at 5 seconds\r
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