document.write( "Question 1156645: Solve. Use a graphing calculator if necessary. See Examples 9 - 11. (Objective 8)
\n" ); document.write( "From the top of the building, a ball is thrown straight up with an initial velocity of 64 feet per second. The equation
\n" ); document.write( "s = −16t2 + 64t + 80
\n" ); document.write( " gives the height s of the ball t seconds after it is thrown. Find the maximum height (in feet) reached by the ball and the time (in seconds) it takes for the ball to hit the ground. (Hint: Let s = 0 and solve for t.)
\n" ); document.write( "80 ft
\n" ); document.write( "A rectangular building is 80 ft tall.
\n" ); document.write( "A curved path starts at the top-right side of the building and goes up and to the right past the right edge of the building. The path gets less steep as it reaches a high point, and then it goes down and to the right, getting steeper as it goes.
\n" ); document.write( "The ball is at the end of the path midway between the top of the building and the ground, and its height above the ground is labeled s.
\n" ); document.write( "A vertical dashed line starts at the ball and goes down to touch the ground.
\n" ); document.write( "The maximum height reached by the ball is-
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Algebra.Com's Answer #779410 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "            Let me start explaining DEFICIENCIES in your post and in your knowledge.\r
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\n" ); document.write( "\n" ); document.write( "            At the beginning, the post says that the ball is thrown STRAIGHT UP with the velocity of 64 ft per second.\r
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\n" ); document.write( "\n" ); document.write( "            It exactly corresponds to the equation for the height.\r
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\n" ); document.write( "\n" ); document.write( "            But then you start describing the parabolic trajectory.\r
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\n" ); document.write( "\n" ); document.write( "            In this problem, THERE IS NO parabolic trajectory in space: there is ONLY the move VERTICALLY up
\n" ); document.write( "            and then VERTICALLY dawn.\r
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\n" ); document.write( "\n" ); document.write( "            And the reasonable assumption is that the person is standing near the edge of the roof.\r
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\n" ); document.write( "\n" ); document.write( "            After this explanation, I am ready to present the solution.\r
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document.write( "The function  H(t) = -16t^2 + 64t + 80  is a quadratic function, whose plot is a parabola opened down.\r\n" );
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document.write( "This quadratic function has the maximum at the value of its argument  t = , where \"a\" is the coefficient at t^2\r\n" );
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document.write( "and \"b\" is the coefficient at t.\r\n" );
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document.write( "In your case, a= -16,  b= 64, so the function gets the maximum at  t =  = 2.\r\n" );
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document.write( "So, the ball gets the maximum height 2 seconds after is is thrown straight up. \r\n" );
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document.write( "To calculate the maximum height, substitute t= 2 seconds into the given formula\r\n" );
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document.write( "    H(t) = -16*2^2 + 64*2 + 80 = 144 feet.\r\n" );
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document.write( "Now the last question: when the ball hits the ground.\r\n" );
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document.write( "For it, you need to equate H(t) to zero, which is the ground level\r\n" );
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document.write( "    H(t) = 0,  or  -16*t^2 + 64t + 80 =0.\r\n" );
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document.write( "Simplify the equation\r\n" );
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document.write( "    16t^2 - 64t - 80 = 0\r\n" );
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document.write( "cancel the common factor 16\r\n" );
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document.write( "    t^2 - 4t - 5 = 0\r\n" );
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document.write( "and factor the left side\r\n" );
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document.write( "    (t-5)*(t+1) = 0.\r\n" );
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document.write( "The only positive root t= 5 is the solution.  The ball will hit the ground in 5 seconds.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved (with complete explanations).\r
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\n" ); document.write( "\n" ); document.write( "On finding the maximum/minimum of a quadratic function, see the lessons \r
\n" ); document.write( "\n" ); document.write( "    - HOW TO complete the square to find the minimum/maximum of a quadratic function\r
\n" ); document.write( "\n" ); document.write( "    - Briefly on finding the minimum/maximum of a quadratic function\r
\n" ); document.write( "\n" ); document.write( "    - HOW TO complete the square to find the vertex of a parabola\r
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\n" ); document.write( "\n" ); document.write( "On solving similar problems to yours in this post, see the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Problem on a projectile moving vertically up and down\r
\n" ); document.write( "\n" ); document.write( "    - Problem on an arrow shot vertically upward\r
\n" ); document.write( "\n" ); document.write( "    - Problem on a ball thrown vertically up from the top of a tower \r
\n" ); document.write( "\n" ); document.write( "    - Problem on a toy rocket launched vertically up from a tall platform\r
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\n" ); document.write( "\n" ); document.write( "Notice that you came to the forum without having right conceptions,\r
\n" ); document.write( "\n" ); document.write( "and you got absolutely full and clear solution, explanation and instructions.\r
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\n" ); document.write( "\n" ); document.write( "And you got the reading to wide your horizon.\r
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