Let AD and BC be two vertical poles at A and B respectively on a horizontal ground. If AD = 8 m, BC

Q: JEE Main 2023 Height and Distance: Let AD and BC be two vertical poles at A and B respectively on a horizontal ground. If AD = 8 m, BC ...

The correct answer is 2. (MD) 2 + (MC) 2 = h 2 + 64 + (h – 10) 2 + 121 = 2h 2 – 20h + 64 + 100 + 121 = 2(h 2 – 10h) + 285 = 2(h – 5) 2 + 235 It is minimum if h = 5.

Question

Let AD and BC be two vertical poles at A and B respectively on a horizontal ground. If AD = 8 m, BC = 11 m and AB = 10 m; then the distance (in meters) of a point M on AB from the point A such that MD 2 + MC 2 is minimum is .

Accepted Answer

(MD) 2 + (MC) 2 = h 2 + 64 + (h – 10) 2 + 121 = 2h 2 – 20h + 64 + 100 + 121 = 2(h 2 – 10h) + 285 = 2(h – 5) 2 + 235 It is minimum if h = 5.

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