(a) We can use a simple kinematic equation to find the speed of the stone when it reaches a height of 11 meters.
v^2 = (v0)^2 - 2gy
v = sqrt{ (18 m/s)^2 - (2)(9.8 m/s^2)(11 m) }
v = 10.4 m/s
The speed is 10.4 m/s when the stone reaches a height of 11 meters.
(b) We can use a simple kinematic equation to find the time it takes for the stone's speed to decelerate to 10.4 m/s.
t = (v - v0) / g
t = ( 10.4 m/s - 18 m/s ) / (-9.80 m/s^2)
t = 0.7755 seconds
It takes 0.7755 seconds for the stone to reach a height of 11 meters, where the speed is 10.4 m/s.
