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Class 12 Applications Of Derivatives · Short Answer2 Marksrelated_rates

Class 12 Maths · Applications Of Derivatives · Short Answer #39

A 5 m ladder leans against a wall. Its foot moves away at 2 cm/s. Find the rate at which its top descends when the foot is 4 m from the wall.
Ladder against a vertical wall
Ladder against a vertical wall

✅ Step-by-Step Solution

Final Answer: 8/3 cm/s
  1. In centimetres, x²+y²=500²; at x=400, y=300 and ẋ=2.
  2. Differentiating gives xẋ+yẏ=0, so ẏ=−400·2/300=−8/3 cm/s.
  3. The height decreases at 8/3 cm/s.

📋 CBSE Stepwise Marking Scheme

  • [0.5 marks] In centimetres, x²+y²=500²; at x=400, y=300 and ẋ=2.
  • [1 mark] Differentiating gives xẋ+yẏ=0, so ẏ=−400·2/300=−8/3 cm/s.
  • [0.5 marks] The height decreases at 8/3 cm/s.

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