Question

A stone is dropped under gravity from rest from a height h and it travels a distance 9h/25 in the last second. What is the height H?

Answer 1

H=gt²/2
16H/25 =g(t-1)²/2

16gt²/2•25 = g(t²-2t+1)/2
16t²=25t²- 50t +25
9 t²-50t +25=0
t= (50±sqrt(2500-4•9•25))/18=(50±40)/18
t₁=5 s, t₂=0.55s ( extraneous root since is less than 1 second)

H= gt²/2 =9.8•5²/2=122.5 m

Answer 2

56