please help me!??????!!!!!?

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

First part
Take negative accelaration, gravity=10m/s2
Initial velocity = u
final velocity = v
time, t = 0.5seconds

height = h

now we know that

final velocity = initial velocity + a production of accelaration and gravity

or v= u + at
Substituting values
0 = u+ (-10 x 0.5)
solving you get
u = 5 m/s


Using newton's law of motion


h= ut + (at2)/2
h = 5t + (-10 x t2)/2
h = 5t - 5t2, so here is your equation

second part
as for the ball hitting the ground

now yr accelaration is positive, and initial velocity is zero

so u again use

h = ut + at2/2

h= 8m, as given in the problem

so 8 = 0 + 10 x t2/2
8 x 2/10 = t2

t2= 8/5, solve that and u have yr answer

i assumed you are allowed to use newton's laws of motion, and also that u were not to arrive at equations using differentiation