help with this 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

equation:
h = u*t + 1/2 * a * t * t --eqn 1.
where
h = height = 8 feet = 2.4384 meters
u = initial velocity, we need to find that
a = acclereation, here it's negative gravity, a = -9.8 m/s^2
t = time

first, find u. put everything else in the eqn .. h=2.4384, a = -9.8 , t = 0.5
we get
2.4384 = u*0.5 - 1/2 * 9.8 * 0.5^2
u = 7.3268 m/sec

now put values of u & a in eqn 1 to get the time-dependent eqn:

h = 7.3268 *t - 4.9 * t *t
that's the first answer!

b) ball takes as much time to go up as to go down. (assuming kim threw it from ground level!)
so if it took 0.5 secs reach upmost, it's gonna take another 0.5 secs after that to hit the ground
so total time to hit ground = 0.5+0.5 = 1 second