Question

A particle is released from rest from a tower of height

3h the ratio of times to fall equal heights h,i.e ,t1:t2:t3

A) root 3:root2:1

B)3:2:1

C)9:4:1

D)1:(root2-1):(root3-root2

Select correct option

Answer 1

We know that

s = ut + (1/2)at^2

here

u = 0

a = g

now for the first case, the total distance travelled in the t1second

s1 = (1/2)gt1^2

similarly the distance travelled after 2 ad 3 seconds respectively

s2 = (1/2).g.(t1 + t2)^2

s3 = (1/2).g.(t1 + t2 + t3)^2

so, the ratio of the height will be

s1 : s2 : s3 = 1 : 2 : 3 = t1^2 : (t1 + t2)^2 : (t1 + t2 + t3)^2

or

t1 : (t1 + t2) : (t1 + t2 + t3) = 1 : √2 : √3

thus, we get

(t1 : t2 : t3) = 1 : (√2 - 1) : (√3- √2)
Option D