A ball is thrown vertically upward with a
speed of 23.7 m/s from a height of 2.0 m.
How long does it take to reach its high-
est point? The acceleration of gravity is
9.81 m/s2
2) How long does the ball take to hit the ground after it reaches its highest point?
(1) The ball reaches its highest point when g*t = 23.7 m/s, because that is where the vertical velocity component becomes zero.
t = 23.7/g = 23.7/9.8 = 2.4 seconds. It matters not what height the ball is thrown from, for this part.
(2) The highest point will be at a distance
Vo*t - (g/2)t^2 = 28.7 m above where it was thrown from. That will be 30.7 m above the ground.
Now all you have to do is compute the new time required to fall that distance. Call it t'
Use 30.7 m = (g/2)*t'^2 and solve for t'.