Question

A stone is allowed to fall freely from rest.the ratio of time taken to fall through the first metre yo second metre distance is

Answer 1

v₀ = initial velocity for the stone = 0 m/s

a = acceleration = 9.8 m/s²

y₁ = 1 m

y₂ = 2 m

t₁ = time taken to travel distance "y₁"

t₂ = time taken to travel distance "y₂"

using the equation

y₁ = v₀ t₁ + (0.5) a t₁²

1 = (0) t₁ + (0.5) (9.8) t₁²

t₁ = 0.45 sec

using the equation

y₂ = v₀ t₂ + (0.5) a t₂²

2 = (0) t₂ + (0.5) (9.8) t₂²

t₂ = 0.64 sec

time taken to travel first meter = t₁ = 0.45 sec

time taken to travel second meter = t₂ -  t₁ = 0.64 - 0.45 = 0.19 sec

Ratio =  time taken to travel first meter/time taken to travel second meter

Ratio = 0.45/0.19

Ratio = 2.4

Answer 2

so the answer will be (√2+1)