T = 2π√(R/g) ≈ 5076 s ≈ 84.6 min for r ≈ Earth radius. Standard result. Memory aid: 'Low orbit: ~84 min; geostationary: 24 hours'. Orbital mechanics fact frequently tested in competitive exams.
Explanation:
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Explanation:
The maximum height H = (u^2 * sin^2(theta)) / 2g. The horizontal range R = (u^2 * sin(2theta)) / g. For an angle of 45 degrees, sin(45) = 1/sqrt(2) and sin(90) = 1. H = (u^2 * 0.5) / 2g = u^2 / 4g. R = u^2 / g. Therefore, H/R = (u^2/4g) / (u^2/g) = 1/4. The ratio is 1:4.
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