Question

A freely falling body , falling from a tower height h covers a distance h/2

Answer 1

Time taken to fall freely a distance h meters from rest =✓2h/g units …………..(1)

According to question, time taken to fall h/2 from start = (✓2h/g)-1 units…………(2)

But from (1), time taken to fall height h/2 meters = ✓2×(h/2)/g = ✓h/g units….(3)

Equating (2) and (3) we get ,

✓2h/g -1 =✓h/g

✓2 ✓h/g -✓h/g = 1

✓2 ✓h/g -✓h/g = 1

✓h/g = 1/(✓2–1)= ✓2+1 …..( rationalising)

h/g = 2+1+2✓2= 3+2✓2….….(squaring)

Therefore, h = (3+2✓2)g units (ANS)

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