The blades of a windmill turn on an axis that is 35 feet above the ground. The blades are 10 feet long and complete two rotations every minute. Which of the following equations can be used to model h, the height in feet of the end of one blade, as a function of time, t, in seconds? Assume that the blade is pointing to the right, parallel to the ground at t = 0 seconds, and that the windmill turns counterclockwise at a constant rate.
Answers
Answer:
(c) h = 10sin(π15t)+35
Explanation:
The given options are
a) h = −10sin(π15t)+35
b) h = −10sin(πt)+35
c) h = 10sin(π15t)+35
d) h = 10sin(πt)+35
Now lets check the options one by one and choose our correct option.
at time t=0, the blade is horizontal. Hence, at t = 0, h = 35 which is applicable for all the options here.
In one minute, they complete two rotations. Therefore in 30 seconds, the blades will complete one rotation. and in 15/2 seconds they will complete 1/4 rotation Thus from time t = 0 to t = 15/2, the blade will be vertically up. In this case its height should be 35 + 10 = 45 feet. Now lets check the given options.
If we put t=15/2 in the options
Option (a) gives h = 25
Option (b) gives h = -10sin(15/2) + 35
Option (c) gives h = 45
Option (d) gives h = 10sin(15/2) + 35
Thus option (c) is correct.
Answer: C
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