Robert loves to dive . he joined the diving team . the diving board is feet above the water . if he jumps off the diving board as high as he can ( 10ft/s ) .how high above the water does he get ? and how long is he in mid air before he hits the water ?

Answer 1

It would help if you proofread your questions before you posted them.

How high is the diving board?

Answer 2

You have a typo and don't state how high above the water the diving board is.
I will give it an arbitrary value of 6 ft.
So the equation of height is

h = -16t^2 + 10t + 6, where h is in ft and t is in seconds , where t ≥ 0

for a max height, we need the vertex of that parabola
the t of the vertex is -b/(2a) = -10/-32 = .3125 seconds
and the height is -16(.3125^2) + 10(.3125) + 6
= 7.5625 ft

for how long in the air,
You want h = 0
-16t^2 + 10t + 6 = 0
divide by -2
8t^2 - 5t - 3 = 0
Using the formula
t = (5 ± √(25 - 4(8)(-3))/16
= (5 ± √121)/16
= -1/2 or 1

He will be in the air for 1 second

Adjust the above solution to whatever the height of the board is above the water.
I picked the 6 since I knew it would work out nice at the end.