A farmer's tractor pulls a rope of length 12 m attached to a bale of hay through a pulley that is 7 m above the ground. The vertical distance between the tractor and the pulley (the distance from P to Q) is 6 m. The tractor is moving to the left at a rate of 3 m/s, which causes the bale of hay to rise off the ground. Use this information to answer the following questions.

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Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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​(f) The rate of change​ (with respect to​ time) of which variable is equal to the rate at which the bale of hay is​ rising?
 
A.z
 
B.x
 
C.h
 
D.y
(g) When the horizontal distance between the tractor and the bale of hay is 4m, the bale of hay is rising off the ground at a rate of 
pulley
y
Наy
h
A farmer's tractor pulls a rope of length 12 m attached to a bale of hay through a pulley that is 7 m
above the ground. The vertical distance between the tractor and the pulley (the distance from P to Q)
is 6 m. The tractor is moving to the left at a rate of 3 m/s, which causes the bale of hay to rise off the
ground. Use this information to answer the following questions.
Transcribed Image Text:pulley y Наy h A farmer's tractor pulls a rope of length 12 m attached to a bale of hay through a pulley that is 7 m above the ground. The vertical distance between the tractor and the pulley (the distance from P to Q) is 6 m. The tractor is moving to the left at a rate of 3 m/s, which causes the bale of hay to rise off the ground. Use this information to answer the following questions.
(a) The rate of change (with respect to time) of which variable is equal to the speed of the tractor?
А. h
О В. х
ОС. у
O D. z
(b) By the Pythagorean theorem, an equation that holds for all time and involves only the variables x and z is:
Your answer must be an equation containing only the following: numbers, variable x, variable z. All numbers must be exact.
(c) Since the length of the rope is constant, an equation that holds for all time and involves only the variables z and y is:
Your answer must be an equation containing only the following: numbers, variable y, variable z. All numbers must be exact.
(d) Since the height of the pulley is constant, an equation that holds for all time and involves only the variables h and y is:
Your answer must be an equation containing only the following: numbers, variable h, variable y. All numbers must be exact.
(e) Combining the equations from part (b), part (c), and part (d), we get the following equation that holds for all time and involves only the variables x and h:
Your answer must be an equation containing only the following: numbers, variable h, variable x. All numbers must be exact.
Transcribed Image Text:(a) The rate of change (with respect to time) of which variable is equal to the speed of the tractor? А. h О В. х ОС. у O D. z (b) By the Pythagorean theorem, an equation that holds for all time and involves only the variables x and z is: Your answer must be an equation containing only the following: numbers, variable x, variable z. All numbers must be exact. (c) Since the length of the rope is constant, an equation that holds for all time and involves only the variables z and y is: Your answer must be an equation containing only the following: numbers, variable y, variable z. All numbers must be exact. (d) Since the height of the pulley is constant, an equation that holds for all time and involves only the variables h and y is: Your answer must be an equation containing only the following: numbers, variable h, variable y. All numbers must be exact. (e) Combining the equations from part (b), part (c), and part (d), we get the following equation that holds for all time and involves only the variables x and h: Your answer must be an equation containing only the following: numbers, variable h, variable x. All numbers must be exact.
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