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Question

A ladder is resting with the wall at an angle of 30 degrees. A man is ascending the ladder at the rate of 3 ft/sec.

His rate of approaching the wall is


A

3 ft/sec

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B

32 ft/sec

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C

24 ft/sec

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D

32 ft/sec

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Solution

The correct option is B

32 ft/sec


Finding the rate of approaching the wall:

The ladder makes 30° with the wall.

And wall and ground makes 90° angle.

So the ladder makes[180-(90+30)]=60° with the ground.

It is shown that the man is ascending at the rate of 3

So, the component of this rate along the horizontal is given by:

3cos(60)=3(12)=32feet\seconds

Hence, his rate of approaching the wall is 32 feet/seconds, option (B) is correct option.


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