A stone is thrown vertically upward with a speed of 15.0 m/s from the edge of a cliff 75.0 m high?

Take g = 9.81 m/s², and take all downward quantities to be positive.

Initial velocity, u = -15.0 m/s (negative due to it is upward)
Displacement, s = 75.0 m
Acceleration, a = 9.81 m/s²

s = ut + (1/2)at²
75.0 = (-15.0) × t + (1/2) × 9.81 × t²
4.905t² - 15.0t - 75.0 = 0
t = [15.0 ± √(15.0² + 4 × 4.905 × 75.0)] / (2 × 4.905) s
Time taken, t = 5.73 s or t = -2.67 s (rejected)
5.73 s later, the stone reaches the bottom of the cliff.

v² = u² + 2as
v² = (-15.0)² + 2 × 9.81 × 75.0
v = √[(-15.0)² + 2 × 9.81 × 75.0]
Final velocity, v = 41.2 m/s
Its speed just before hitting the ground = 41.2 m/s

Impact speed Vi = √Voy^2+2gh = √15^2+19,6*75 = 41,17 m/sec
-75 = 15*t-4.903t^2
flying time t = (15+√15^2+19.612*75)/9.806 = 5.73 sec