real world application 3

label Mathematics
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   ferris wheel rotates counter clockwise, how many seconds will it take for your seat to reach a height of 75 meters?

Oct 16th, 2017

Answering this question requires more information. the radius (R) and the speed of rotation (v). the starting point of the seat can be assumed to be at the bottom of the wheel (0 m).

75 = R - R*cos(theta). from here, theta can be calculated. (will give two values, which is fine as seat reaches the height of 75 m twice in one rotation) (careful, use value of theta in radians, not degrees)

Now, to rotate a full circle (an angle of 2*pi), it takes 2*pi*R/v time. Therefore to travel 'theta' angle, it will take

(2*pi*R/v)*theta*/(2*pi), which can be simplified as

R*theta/v secs This will give you two possible values of time, as seat reaches 75 m height twice in one rotation.

Nov 27th, 2014

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