Time taken (t1) by freely falling body to travel first 5 m is given as, s‌=ut1+‌
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gt12 5‌=0×t1+‌
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×10×t12 ⇒‌‌t1‌=1s Time taken ( t′ ) to travel 10 m . 10‌=0×t1′+‌
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×10×t′2 ⇒‌‌t′‌=√2s ∴ Time taken (t2) to travel next 5 m , t2=t′−t1=(√2−1)s Time taken (t′′) to travel 15 m , 15‌=0×t′′+‌
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×16×(t′′)2 15‌=5(t′′)2 ∴‌‌t′′‌=√3s Thus, time taken (t3) to travel lost 5 m t3‌=t′′−t′=√3−√2 ∴t1:t2:t3‌=1:(√2−1):(√3−√2)