Multiple choice

Anil looked up at the top of a lighthouse from his boat and found the angle of elevation to be 30 degrees. After sailing against the direction of stream at the speed of 25m/s for 2.5seconds towards the lighthouse, he found that the angle of elevation changed to 45 degrees. Find the height of the lighthouse, if speed of stream is 5m/s.

  1. 25(√3 +1) m

  2. 50(√3 – 1) m

  3. 25(√3 – 1) m

  4. 50(√3 +1) m
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A Correct answer
Explanation

Sailing at 25 m/s for 2.5 seconds covers 62.5 m against a 5 m/s stream, so effective horizontal distance = (25-5) × 2.5 = 50 m. At 30° elevation: tan30° = h/d₁, so d₁ = h/√3. At 45° elevation: tan45° = h/d₂, so d₂ = h. Since d₁ - d₂ = 50 m, we get h/√3 - h = -50, giving h = 50√3/(√3-1) = 25(√3+1) m.

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