document.write( "Question 1124245: Can you help me to solve and understand this problem. please:
\n" ); document.write( "A Ferris wheel 70 feet in diameter completes one revolution every 58 seconds. Its central point is 40 feet above the ground.
\n" ); document.write( "a) write a sinusoidal function H(t) to model a rider's height above ground as a fusion of time t in seconds.
\n" ); document.write( "b) how long does. it take a rider to go from the lowest point of travel to 61 feet above the ground?
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Algebra.Com's Answer #740591 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
If you spin a radius vector, $\"+r+\"$ , at the origin,
\n" ); document.write( "It traces out a sine wave plotted on the time axis.
\n" ); document.write( "It has a -r to +r height, so the height is $\"+2r+\"$
\n" ); document.write( "——————
\n" ); document.write( "In your problem, $\"+2r+=+70+\"$ and $\"+r+=+35+\"$
\n" ); document.write( "If the Ferris wheel was at ground level, the
\n" ); document.write( "function would be $\"+f%28t%29+=+35%2Asin%28+%28+2pi%2F58+%29%2At+%29+\"$ ,
\n" ); document.write( "but they want the center $\"+40+\"$ ft above ground,
\n" ); document.write( "So the function is: $\"+H%28t%29+=+35%2Asin%28+%28+2pi%2F58+%29%2At+%29+%2B+40+\"$
\n" ); document.write( "——————-
\n" ); document.write( "b)
\n" ); document.write( "Find $\"+t+\"$ when $\"+H%28t%29+=+61+\"$
\n" ); document.write( " $\"+61+=+35%2Asin%28+%28+2%2Api%2F58+%29%2At+%29+%2B+40+\"$
\n" ); document.write( " $\"+35%2Asin%28+%28+2%2Api%2F58+%29%2At+%29+=+21+\"$
\n" ); document.write( " $\"+sin%28+%28+2%2Api%2F58+%29%2At+%29+=+.6+\"$
\n" ); document.write( "If this was:
\n" ); document.write( " $\"+sin%28+theta+%29+=+.6+\"$ then, in radians,
\n" ); document.write( " $\"+theta+=+.6435+\"$ radians ( calculator )
\n" ); document.write( "Now I can say:
\n" ); document.write( " $\"+%28+2%2A3.14159%2F58+%29%2At+=+.6435+\"$
\n" ); document.write( " $\"+.10833%2At+=+.6435+\"$
\n" ); document.write( " $\"+t+=+5.9402+\"$ sec
\n" ); document.write( "———————————
\n" ); document.write( "Here’s a plot:
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\n" ); document.write( "Note that with this curve, you would have to get on
\n" ); document.write( "the Ferris wheel at the 58 sec time. If you used -cos instead of
\n" ); document.write( "sin, then you get on at the zero time mark
\n" ); document.write( "Hope all this helps\r
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