Question

If a body travels half of its path in the last second of its fall from rest; find the time and height of its fall?

Answer 1

Time

Suppose the body travelled total t second and the height is h then we have
1/2gt^2 = h
and
1/2 g(t-1) ^ 2=h/2=1/4 gt^2
=>g(t^2 + 1 - 2t) = 1/2gt^2
=>1/ 2gt ^2- 2gt+g=0
=> 3.41
As the body travelled more than 1s so answer is 3.41s