Aboat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley on the dock that is 1 m higher than the bow of the boat. if the rope is pulled in at a rate of 1 m/s, how fast is the boat approaching the dock when it is 7 m from the dock?

The boat is approaching the dock when it is 7 m from the dock at a rate of 1.0102 m

Explanation:

The situation is drawn in the image shown below.

From the image,

Applying Pythagorean theorem as:

a² + 1² = b² .....1

Differentiation both side w.r.t. time as:

or,

...2

Given:

The rate of the pulling of the rope in = 1 m/s

Thus,

We have to find when a = 7 m

Using equation 1 to calculate b as:

7² + 1² = b²

b = √50 m

Using equation 2 as:

Thus,

Thus, the boat is approaching the dock when it is 7 m from the dock at a rate of 1.0102 m

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