Difference between revisions of "2002 AMC 10B Problems/Problem 24"
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path ferriswheel=Circle(O,r); | path ferriswheel=Circle(O,r); | ||
draw(ferriswheel); | draw(ferriswheel); | ||
| − | draw(O--A); draw(O--C); draw(B--C); | + | draw(O--A); draw(O--C); draw(B--C); draw(A--C); |
pair[] ps={A,B,C,O}; dot(ps); | pair[] ps={A,B,C,O}; dot(ps); | ||
label("$O$",O,N); label("$A$",A,S); label("$B$",B,W); label("$C$",C,SE); | label("$O$",O,N); label("$A$",A,S); label("$B$",B,W); label("$C$",C,SE); | ||
Revision as of 13:06, 7 August 2018
Problem 24
Riders on a Ferris wheel travel in a circle in a vertical plane. A particular wheel has radius 
feet and revolves at the constant rate of one revolution per minute. How many seconds does it take a rider to travel from the bottom of the wheel to a point 
vertical feet above the bottom?
Solution
![[asy] unitsize(1.5mm); defaultpen(linewidth(.8pt)+fontsize(10pt)); dotfactor=4; pair O=(0,0), A=(0,-20), B=(0,-10), C=(10sqrt(3),-10); real r=20; path ferriswheel=Circle(O,r); draw(ferriswheel); draw(O--A); draw(O--C); draw(B--C); draw(A--C); pair[] ps={A,B,C,O}; dot(ps); label("$O$",O,N); label("$A$",A,S); label("$B$",B,W); label("$C$",C,SE); label("$10$",(O--B),W); label("$10$",(A--B),W); label("$20$",(O--C),NE); [/asy]](http://latex.artofproblemsolving.com/3/7/e/37e56fa9375622b7173da2e667258b8e39157603.png)
We can let this circle represent the ferris wheel with center 
and 
represent the desired point feet above the bottom. Draw a diagram like the one above. We find out 
is a 
triangle. That means 
and the ferris wheel has made 
of a revolution. Therefore, the time it takes to travel that much of a distance is 
of a minute, or seconds. The answer is 
. Alternatively, we could also say that 
is congruent to by SAS, so 
is 20, and 
is equilateral, and
See also
| 2002 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 23 |
Followed by Problem 25 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AMC 10 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
