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Physics · MOTION IN A STRAIGHT LINE
हिन्दीA body falling freely under gravity (\( g = 10 \text{ m/s}^2 \)) from rest at height \( H \) covers a distance in its final second of motion that is equal to the distance covered by it in the first \( 3.0 \text{ seconds} \) of its fall. Determine the total height \( H \).
Correct answer · Option 4
\( 125 \text{ m} \)
Explanation
Distance in first 3 seconds: \( y_3 = \frac{1}{2}(10)(3^2) = 45 \text{ m} \). Distance in \( n^{\text{th}} \) second: \( D_n = \frac{g}{2}(2n - 1) = 5(2n - 1) \). Setting \( 5(2n - 1) = 45 \implies 2n - 1 = 9 \implies n = 5 \text{ s} \). Total height \( H = \frac{1}{2}(10)(5^2) = 125 \text{ m} \).
