(2) Rate Of Change Assignment
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- Aha! I remember that the ferris wheel takes 16 minutes for 1 rotation, is 40 meters tall, and starts 3 meters off the ground!
- Ahh we're almost at the top... I don't know if I am going to vomit! Should I face you or away from you?
- This means that the period is 16 minutes, and since we start 3 meters off the ground, the baseline is at 23 meters, and amplitude is 20! Since we started at the bottom, the function for this ferris wheel is "-20cos(pi/8 x) + 23)"
- Um...
- Uh oh! We have been on the ride for almost 5 minutes, and I still don't know if we will have a good first kiss! I must determine the wheel'sinstantaneous rate of change (IROC) at exactly 5 minutes!
- Hey Julia, can I kiss you?
- Through many calculations, I determined that the exact moment of our supposed kiss, we will be travelling at around 7.256m/min upwards, which is slower than the maximum of 8m/min, meaning that I should kiss her!
- Sure Colby! You know that I love smart mathematicians!
- To determine average speed of wheel (AROC), I will substitute the y value at 0m min 40m max height into the function, then compare x y values with (y2-y1) ÷ (x2-x1)
- Aha! Julia I can face you without vomiting on you because I know that our slower speeds will prevent me from getting motion sickness!
- Knowing these two points isneeded to determine average rate of change. With this equation, I know that our average speed from the bottom to the top of the wheel is 5m/min, which is slower than 5.5m/min... So I won't vomit!
- Wonderful! I guess you figured out that we have been moving slower than the birds at this height!Also, I was wondering if you would like to go on another date next week?
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