help with this algebra problem??

Question

I need help with this algebra problem...i have no idea how to solve it.........Kim throws a ball straight up into the air. The ball reaches a maximum height of 8 feet above the ground in .5 seconds.
a) Find the equation giving the ball's height (h) as a function of time (t).
b) When does the ball hit the ground?

Answer 1

a) [{g.(t^2)}/2]=8

or , ut -[{g.(t^2)}/2]=8 , when u = the velocity of throwing

b)
ut -[{g.(t^2)}/2]=h...................(i) , h=the maximum height

u-gt = 0 , or, u=gt ..................(ii) as v= 0 i.e. the velocity of ball at maximum height .

from (i) & (ii) [{g.(t^2)}/2]=h...........(iii)

if T is the time to reach the ball at ground from h height , then ,

[{g.(T^2)}/2]=h ............(iv)

from (iii) & (iv) T=t
i.e. the time to reach at h = the time to reach the ball at ground from h height .
therefore ball return after 10sec after thorwing.