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Q3.22: NCERT Physics - Part 1 MOTION IN A PLANE 3.22 Solution: An aircraft is flying at a height of 3400 m above the ground.…
⚠️ Common Exam Traps & Conceptual Pitfalls
Students often split the given 30° subtended angle into two 15° angles and use tan 15° = (d/2)/height, implicitly assuming the aircraft is equally distant from the observer at the start and end of the 10 s interval. This symmetry is not guaranteed; the correct approach must relate the two sight‑lines via tan θ₁ = x₁/3400 and tan θ₂ = x₂/3400 with θ₂‑θ₁ = 30°, and only use the half‑angle if the problem explicitly states the aircraft passes directly overhead at the midpoint.
An aircraft is flying at a height of 3400 m above the ground. If the angle subtended at a ground observation point by the aircraft positions 10.0 s apart is 30�, what is the speed of the aircraft?
Step-by-Step Verified Solution
**Answer:** Speed = 182.4 m/s.
**Step-by-Step Explanation:**
Let the horizontal distance covered in 10 s be d.
tan(15�) = (d/2)/3400 _ d/2 = 3400 _ tan(15�) = 911 m _ d = 1822 m.
Speed = 1822/10 = 182.2 m/s.
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