document.write( "Question 1190706: A Ferris wheel that is 18 meter in diameter makes a revolution in 5 seconds. If the center is 10m above the ground, how long does a rider reach a height of 15 m? \n" ); document.write( "

Algebra.Com's Answer #822421 by ikleyn(52858) $\"\"$ $\"About$

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\n" ); document.write( "A Ferris wheel that is 18 meter in diameter makes a revolution in 5 seconds.
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document.write( "Our Ferris wheel has the radius of 18/2 = 9 meters and the lowest position at the height of 1 meter over the ground.\r\n" );
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document.write( "Let's consider this Ferris wheel as rotated anti-clockwise.\r\n" );
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document.write( "So, it rotates from position 6 pm (the hour hand) anti-clockwise to the position 3 pm by 90 degrees,\r\n" );
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document.write( "reaching the height of 10 meters above the ground, and then rotates for some additional angle \"a\"\r\n" );
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document.write( "anti-clockwise, such that the height is 15-10 = 5 meters above the level of the center, which is 10 meters above the ground.\r\n" );
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document.write( "This angle \"a\" satisfies equation  sin(a) =  = 0.555556,  so  a = arcsin(0.555556) = 33.75 degrees.\r\n" );
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document.write( "Thus the wheel turns/rotates the angle  90 + 33.75 degrees = 123.75 degrees, total.\r\n" );
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document.write( "The angular velocity of the wheel is 360 degrees in 5 seconds, or   = 72 degrees per second.\r\n" );
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document.write( "So, it will take   = 1.72 seconds for the rider to get the height of 15 meters above the ground,\r\n" );
document.write( "starting from the lowest position.\r\n" );
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document.write( "ANSWER.  1.72 seconds, approximately.\r\n" );
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