document.write( "Question 880725: suppose that you drop a ball from a window 45m above the ground. The ball bounces to 65% of it previous height wit each bounce. Find the total number of metres the ball travels between the time it is dropped and the 8th bounce. \n" ); document.write( "

Algebra.Com's Answer #531648 by Edwin McCravy(20054) $\"\"$ $\"About$

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suppose that you drop a ball from a window 45m above the ground. The ball bounces to 65% of it previous height wit each bounce. Find the total number of metres the ball travels between the time it is dropped and the 8th bounce.
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document.write( "It is not clear what is meant exactly by \r\n" );
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document.write( "\"between the time it is dropped and the 8th bounce.\".  \r\n" );
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document.write( "Does this mean that we are to determine the number of meters the ball\r\n" );
document.write( "has traveled when it hits the ground the 8th time? or the 9th time?\r\n" );
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document.write( "We really cannot be sure!  You will have to ask your teacher.\r\n" );
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document.write( "I will arbitrarily assume it is like the drawing below, and find the distance\r\n" );
document.write( "the ball has traveled when it hits the ground for the 8th time, not the 9th.  \r\n" );
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document.write( "As you see from the sketch, there are 8 \"falls\" and 7 \"rises\".\r\n" );
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document.write( "The \"falls\" form a geometric series, with a₁=45, r=0.65, n=8\r\n" );
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document.write( "So the sum of the 8 \"falls\" is 124.47456669m.\r\n" );
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document.write( "The sum of the \"rises\" is the same as the sum of the \"falls\" except for the \r\n" );
document.write( "first \"fall\" of 45m.\r\n" );
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document.write( "So the sum of the rises is 124.47456669m - 45m = 79.47456669m\r\n" );
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document.write( "Distance the ball has traveled when it hits the ground the 8th time =\r\n" );
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document.write( "124.47456669m + 79.47456669m = 203.9491334m.\r\n" );
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document.write( "Edwin

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