- 8.
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- Let x = distance (in feet) that Phil Anthropist has traveled,
y = height above ground (in feet) of a white spot on the rim of a hamster wheel that Phil is transporting to a charity.
- Other useful facts: Phil drives at a steady 30 mph (_____ ft/sec; fill this in if you can; otherwise raise hand for a hint). The hamster wheel has a diameter of 6 inches and has an axle that is positioned in Phil’s car at a height of 2.7 ft above ground level. The hamster is a very smooth fellow who runs at a steady speed that causes the wheel to spin with a uniform rotational speed of 2 revolutions per second. Finally, the white spot starts at the 3 o’clock position (i.e., toward the front of the car as we begin this exciting adventure). Since the hamster is facing forward, the white spot will initially go (circle one) upward / downward.
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(a) |
- Is y = f (x) a periodic function? _____ Why or why not? __________________
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(b) |
- What is the period of f ? (Remember, both x and y are measured in feet.)
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(c) |
- Is f approximately sinusoidal?
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(d) |
- State f (0) in words and with a numeric value.
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(e) |
- State f (5.5) in words and with a numeric value. Hint: 5.5 equals 1/8 of 44.
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(f) |
- Find values of A, B, C, and D. You must show work for at least one of these.
A =
B =
C =
D =
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(g) |
- Define the function f (x).
f (x) =
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(h) |
- Using your calculator to help, sketch f (x) neatly. Please use graph paper if possible. Be sure to indicate the features A, B, C, and D on your sketch.
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