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Ladder against a wall, foot pulled away at a given rate: how fast the top slides down

The same question, asked 3 times: 15 May 2023 S1*, 10 May 2024 S1*, 11 May 2024 S2. Every wording below, oldest first.

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  1. Question 1

    15 May 2023 S1

    140
    A ladder 5 m in length is leaning against a wall. The bottom of the ladder is pulled along the ground away from the wall, at the rate of 22 m/sec. How fast is the height on the wall decreasing when the foot of the ladder is 4 m away from the wall?

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  2. Question 2

    10 May 2024 S1

    106
    A ladder of length 17 m rests with one end against a vertical wall and the other on the level ground. If the lower end slips away at the rate of 1 m/sec, then when it is 8 m away from the wall, its upper end descends at

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  3. Question 3

    11 May 2024 S2

    125
    A rod AB, 13 feet long moves with its ends A and B on two perpendicular lines OX and OY respectively. When A is 5 feet from O, it is moving away at the rate of 3 feet/sec. At this instant, B is moving at the rate

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