Question

Find the height from which an object was dropped (zero initial velocity) if the object travels 1/3 of the entire height in the last second only. Assume free fall.

Answer 1

If dropped from height h, we have

y = h - 4.9t^2
so, it takes t = √(h/4.9) seconds to hit the ground.
and we know that
y(t-1) = h/3
h - 4.9(√(h/4.9)-1)^2 = h/3
Now just solve for h