document.write( "Question 1205578: Duane throws a tennis ball in the air. After 1 second, the height of the ball is 53 ft. After 2 seconds, the ball reaches a maximum height of 69 feet. After 3 seconds the height of the ball is 53 ft.
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Algebra.Com's Answer #842476 by ikleyn(52782) $\"\"$ $\"About$

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\n" ); document.write( "Duane throws a tennis ball in the air. After 1 second, the height of the ball is 53 ft.
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\n" ); document.write( "Part A. Write a quadratic function to represent the height of the ball, ℎ, at any point in time, 𝑡.
\n" ); document.write( "Part B. How long will the tennis ball stay in the air? Round your answer to the nearest
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document.write( "We are given that at t= 2 seconds the height is maximum 69 feet.\r\n" );
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document.write( "It means that the quadratic function in vertex form has the formula\r\n" );
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document.write( "    h(t) = a*(t-2)^2 + 69.\r\n" );
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document.write( "In this formula, we have only one unknown parameter \"a\".\r\n" );
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document.write( "To find it, we use the condition h(1) = 53\r\n" );
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document.write( "    53 = a*(1-2)^2 + 69.\r\n" );
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document.write( "It gives\r\n" );
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document.write( "    a*(-1)^2 = 53 - 69\r\n" );
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document.write( "    a = -16.\r\n" );
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document.write( "So, the quadratic function of the height is\r\n" );
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document.write( "    h(t) = -16*(t-2)^2 + 69.    <<<---===  it is the ANSWER to question (A).\r\n" );
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document.write( "At t= 0  (starting moment), the starting height is  \r\n" );
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document.write( "    h(0) = -16*(0-2)^2 + 69 = -16*4 + 69 = 5 ft.\r\n" );
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document.write( "The ball will hit the ground when h(t) = 0\r\n" );
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document.write( "    -16*(t-2)^2 + 69 = 0\r\n" );
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document.write( "    -16*(t-2)^2 = - 69\r\n" );
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document.write( "    16(t-2)^2 = 69\r\n" );
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document.write( "    (t-2)^2 = 69/16\r\n" );
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document.write( "     t - 2 =  = 2.0767 seconds (rounded)\r\n" );
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document.write( "     t = 2 + 2.0767 = 4.0767  seconds  (rounded).\r\n" );
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document.write( "The ball is in the air 4.0767 seconds.\r\n" );
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document.write( "    \r\n" );
document.write( "It is the ANSWER  to question (B).\r\n" );
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