Construction A winch at the top of a 12-meter building pulls a pipe of the same...
Construction A winch at the top of a 12-meter building pulls a pipe of the same length to a vertical position, as shown in the figure. The winch pulls in rope at a rate of −0.2 meter per second. Find the rate of vertical change and the rate of horizontal change at the end of the pipe when y = 6.
Homework Answers
By the Pythagorean Theorem
When y = 6
Then
Then
= 
Now 
Differentiating with respect to t
or 
Now
Differentiating with respect to t
When y = 6, x = 
, S = 12 and 
So
= 
Which is the rate of change of horizontal distance
Now
When y = 6, S = 12 and 
Then
= 
which is the rate of change of vertical distance
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Construction A winch at the top of a 12-meter building pulls a pipe of the same...
A winch at the top of a 12-meter building pulls a pipe of the same length...
A winch at the top of a 12-meter building pulls a pipe of the same length to a vertical position, as shown in the figure. The winch pulls in rope at a rate of -0.6 meter per second (ds/dt = -0.6 m/sec). Find the rate of vertical change and the rate of horizontal change at the end of the pipe when y = 1. (Round your answers to three decimal places.) horizontal -0.5 m/sec vertical m/sec
A winch at the top of a 12-meter building pulls a pipe of the same length...
A winch at the top of a 12-meter building pulls a pipe of the same length to a vertical position, as shown in the figure. The winch pulls in rope at a rate of -0.3 meter per second (ds/dt = -0.3 m/sec). Find the rate of vertical change and the rate of horizontal change at the end of the pipe when y = 4. (Round your answers to three decimal places.) (x, y) 12 m 6 horizontal m/sec vertical m/sec...
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A winch at the top of a 12-meter building pulls a pipe of the same length to a vertical position, as shown in the figure. The winch pulls in rope at a rate of -0.6 meter per second (ds/dt = -0.6 m/sec). Find the rate of vertical change and the rate of horizontal change at the end of the pipe when y = 1. (Round your answers to three decimal places.) horizontal -0.5 m/sec vertical m/sec
A winch at the top of a 12-meter building pulls a pipe of the same length to a vertical position, as shown in the figure. The winch pulls in rope at a rate of -0.3 meter per second (ds/dt = -0.3 m/sec). Find the rate of vertical change and the rate of horizontal change at the end of the pipe when y = 4. (Round your answers to three decimal places.) (x, y) 12 m 6 horizontal m/sec vertical m/sec...
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