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Sliding ladder or rod with ends on two perpendicular lines: related rates

This type of question, asked 6 times: 4 May 2023 S2, 15 May 2023 S1, 10 May 2024 S1, 11 May 2024 S2, 12 May 2024 S1, 12 May 2024 S2. All 6 questions below, oldest first.

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  1. Question 1

    4 May 2023 S2

    133
    A ladder 5 m long rests against a vertical wall. If its top slides downwards at the rate of 10 cm/sec, then the foot of the ladder is sliding at the rate of ___ m/sec, when it is 4 m away from the wall.

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  2. Question 2

    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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  3. Question 3

    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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  4. Question 4

    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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  5. Question 5

    12 May 2024 S1

    131
    A ladder 5 meters long rests against a vertical wall. If its top slides downwards at the rate of 10 cm/s, then the angle between the ladder and the floor is decreasing at the rate of rad./s when its lower end is 4 m away from the wall.

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  6. Question 6

    12 May 2024 S2

    137
    A ladder, 5 meters long, rests against a vertical wall. If its top slides downwards at the rate of 10 cm/s, then the angle between the ladder and the floor is decreasing at the rate of ___ radians/second when its lower end is 4 m away from the wall.

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