document.write( "Question 123608: The data in the table shows the height in metres above the ground of a snowball at various times. Showing all work algebraically, create a function that represents the height of the snowball after t seconds.
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Algebra.Com's Answer #90667 by Edwin McCravy(20055)\"\" \"About 
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The data in the table shows the height in metres above the ground of a snowball at various times. Showing all work algebraically, create a function that represents the height of the snowball after t seconds.
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\n" ); document.write( "HEIGHT(m)---25.1,38.4,41.9,35.6,19.5
\n" ); document.write( "Can someone please help me?
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document.write( "Although it isn't necessary, it is instructive to\r\n" );
document.write( "first plot the 5 points with the times on the x-axis\r\n" );
document.write( "and the heights on the y-axis:\r\n" );
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document.write( "(1,25.1), (2,38.4), (3,41.9), (4,35.6), (5,19.5)\r\n" );
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document.write( "It looks as though a parabola would pass through all those points,\r\n" );
document.write( "so sketch one which passes through all 5 of those points\r\n" );
document.write( "like this:\r\n" );
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document.write( "Now we know that the equation of the height h(t) in meters above the\r\n" );
document.write( "ground of a projectile is given by this formula:\r\n" );
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document.write( "h(t) = h0 + v0t - 4.9t²\r\n" );
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document.write( "where h0 = the original (initial) height above the\r\n" );
document.write( "ground that the projectile was thrown, and\r\n" );
document.write( "v0 = the original (initial) speed in m/s at which\r\n" );
document.write( "the projectile was thrown upward.\r\n" );
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document.write( "So we substitute the first two points. (1,25.1) and (2,38.4): \r\n" );
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document.write( "Substituting t=1 and h(1) = 25.1, we have the equation\r\n" );
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document.write( "h(1) = h0 + v0(1) - 4.9(1)²\r\n" );
document.write( "25.1 = h0 + v0 - 4.9\r\n" );
document.write( "  30 = h0 + v0\r\n" );
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document.write( "Substituting t=2 and h(2) = 38.4, we have the equation\r\n" );
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document.write( "h(2) = h0 + v0(2) - 4.9(2)²\r\n" );
document.write( "38.4 = h0 + 2v0 - 4.9(4)\r\n" );
document.write( "38.4 = h0 + 2v0 - 19.6\r\n" );
document.write( "  58 = h0 + 2v0\r\n" );
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document.write( "So we have this system of two equations in two\r\n" );
document.write( "unknowns:\r\n" );
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document.write( "  30 = h0 +  v0\r\n" );
document.write( "  58 = h0 + 2v0\r\n" );
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document.write( "Can you solve that system for h0 and v0?\r\n" );
document.write( "If not post again asking how.\r\n" );
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document.write( "Answer h0 = 2 meters, v0 = 28 m/s\r\n" );
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document.write( "So substituting in:\r\n" );
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document.write( "h(t) = h0 + v0t - 4.9t²\r\n" );
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document.write( "we find the function h(t) is\r\n" );
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document.write( "h(t) = 2 + 28t - 4.9t²\r\n" );
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document.write( "So really all you needed were two points.\r\n" );
document.write( "The other three were not necessary, but they\r\n" );
document.write( "helped make the problem clearer.\r\n" );
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document.write( "Edwin
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