A ball at rest is dropped from height 'h' and travels a distance of 0.50h in the final 1.00 seconds before it hits the ground.
Find the time and height of its fall.
The Attempt at a Solution
I drew a picture with the knowns:
Obviously I first tried to solve for the total time, but couldn't because I didn't have total displacement of 'h'
So then I tried to solve for 0.50h - h, and got -0.50h = 0t - 1/2(9.8)(t^2) and still left with 2 unknowns.
Then I tried to solve for the bottom half, 0 - 0.50h but I am missing both initial and final velocity therefore there isn't any equation I can use to solve for the lower half since I will always end up with 2 unknown variables again.
I feel like I have exhausted my options because I don't see any other way to go about solving this, since there seems to be only two parts to this problem (the top part of the height and bottom part of the height.