A Ferris wheel has a diameter of 18 yards. Which expression can be used to determine how far around a rider has traveled after the Ferris wheel has gone around 8 times?
Answers
Answer:
Step-by-step explanation:
We can answer the questions without the figure:
a) Since the highest point is 43 feet and the diameter is 40 feet, the lowest point will be 43-40 = 3 feet above ground.
b) The radius of the wheel is 20 feet (=40/2), so that will multiply a sin or cos function.
The center of the wheel is 23 high, so that will be the middle of the sin/cos curve.
It takes 8 seconds per revolution, so we'll want the sin/cos to repeat every 8 seconds.
Lastly it is at the top at 3 seconds. A cos curve is at the top when its argument is 0, so if we use cos with t-3 that should give what we want.
Putting it all together:
height = 23 + 20*cos(360 * (t-3)/8 )
where I've assumed the cos is working in degrees. If it is in radians then in place of 360 put 2pi.
c) we just put 4.5 in for t to get the height at 4.5 s. I'll leave this to you ;-)
(You can roughly check your answer by looking at the sketch in the figure to see if it makes sense.
The expression that can be used to determine the distance traveled by the wheel is 8 × π(18) and the distance is 452.57 yards.
Given:
A Ferris wheel has a diameter of 18 yards.
The Ferris wheel has gone around 8 times
To find:
Which expression can be used to determine how far around a rider has traveled
Solution:
Formula used:
Circumference of circle = πd
where 'd' is the diameter of the circle
From the data, the diameter of the circle = 18 yards
Here, The distance traveled by wheel = Circumference of wheel
Using the formula,
The distance traveled by wheel in 1 revolution = π(18)
Given that the wheel is gone around 8 times
Hence, the total distance traveled = 8 × π(18)
= 144π = 452.57 yards
Therefore,
The expression that can be used to determine the distance traveled by the wheel is 8 × π(18) and the distance is 452.57 yards.
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