Question

How high above the ground is the diving board? The diver leaves the diving board at 6 m/s, jumps 2 meters into the air, and falls to the pool below. The entire time for the dive is 3 seconds.

Answer 1

the vertical velocity is v^2 = 2as = 2*9.8*2
so v=6.26 m/s
Hmmm. Even if he had jumped straight up at 6 m/s, he'd only have gone 1.84 meters into the air.
But let's go with 6 m/s. That means that if the board was at height h,
y = h +6t - 4.9t^2
Since he hit the water at t=3,
h + 6*3 - 4.9*9 = 0
h = 26.1 meters
Now that's a high board!