How to Solve the Kinematics Ratio Problem for a Particle's Journey?

[croslali]

I was given this worksheet from my teacher and well I am finding it really tough so far .. the question below is just crushing my skull .. so i would appreciate it if you guys would guide me through it

"A particle projected from ground takes time 't1' to reach 15/16 H and time 't2' to cover the rest of distance to the ground. If 'H' is the maximum height attained. find the ratio t1: t2

well my options were many ... they were 1:3 ,3:1, 5:3 and 3:5

and well using my knowledge of atleast what i know is: 1)the object has almost reached the max height so the ratio won't be that big 2)i tried using the equations of motions and to no avail i still didnt get anywhere 3)[usin(thetha)(t1)]-[(1/2)g(t1)^2]=(15/16)H 4)and [(usin(thetha)^2]/2g=H

keeping in mind that t2 has to obviously be greater than t1 ... the second and the third options are eliminated ... well it surely can't be 1:3(maybe) .. because that is a really big ratio ...

is there some other extra formula or something other than the common formulae (like max height and range and splitting of vectors)i am supposed to know to solve this question am i missing out anything?

 

[Doc Al]

Try this. How long does it take to fall from a height H? How long does it take to fall a distance H/16?