University of Southern California

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Problem 74

Ferris wheel. The model for the height $h$ of a Ferris wheel car is $h=51+50 \sin 8 \pi t$

where $t$ is measured in minutes. (The Ferris wheel has a radius of 50 feet.) This model yields a height of 51 feet when $t=0$ . Alter the model so that the height of the car is 1 foot when $t=0$ .

Answer

$$\csc \left(\frac{2 \pi}{9}\right)=1.5557$$

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## Discussion

## Video Transcript

hides us with a function that is used to model the height of a Ferris wheel. That function is H equals 51 plus 50 sign of eight pi ti where t is expressed in minutes. We're asked to alter this model so that the height of the car is only one foot when t equals zero. So what is the height of the car? Currently, when t equals zero? Well, h of zero equals 51 plus 50. Sign of a pi times zero. Now sign of a pi. Times zero is the same assigned zero, which equals zero. So h of zero equals 51. And that's 50 more feet than we want our function to be at when t equals zero. So what we can do is subtract 50 from our function. I'm gonna call our new model G of tea, and we'll have GFT equals that 51 minus 50 which is just one was 50. Sign a pie teen and we can prove that this is an appropriate model. By plucking in zero for tea, we see that that equals G of zero of one plus 50 times sign of zero that goes straight to zero and G F zero equals one So g of tea. Is there new model where, instead of adding 51 we just add one, and that gives us the appropriate one foot value in T equals zero.

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