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.
Try each one first, then open its answer.
Question 1
4 May 2023 S2
133A 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.Tap an option to check your answer.
Question 2
15 May 2023 S1
140A 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 m/sec. How fast is the height on the wall decreasing when the foot of the ladder is 4 m away from the wall?Tap an option to check your answer.
Question 3
10 May 2024 S1
106A 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 atTap an option to check your answer.
Question 4
11 May 2024 S2
125A 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 rateTap an option to check your answer.
Question 5
12 May 2024 S1
131A 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.Tap an option to check your answer.
Question 6
12 May 2024 S2
137A 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.Tap an option to check your answer.