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According to the condition, you have a right angled triangle.
One its leg is vertical and has constant dimension v = (3.05 - 0.61) = 2.44 meters.
The other leg is horizontal and its dimension h increases with the rate of
= 4 km/h = 4000/3600 m/s = m/s.
The hypotenuse "c" has the length c = and it is the length of the rope between the pulley and
the car's rear bumper.
The value under the question is the derivative of "c" over time "t"
= (2*h*h'(t))/sqrt*(v^2 + h^2) = (2*h*h'(t))/sqrt*(v^2 + h^2).
You substitute the given data into the formula and calculate
= = 0.993808 m/s.
ANSWER. The rope is going through the pulley at the rate of 0.993808 m/s, under given conditions.
Solved.
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The major lesson to learn from my post is THIS:
After reading the post. you should ask yourself:
What is given and what they want to get from me ?
In this problem, they want you find the derivative of the length of the hypotenuse over the time.
As soon as you understood it, the rest is just a technique.