A stone is thrown vertically upward with a speed of 14.0 m/s from the edge of a cliff 89.0 m high

and...?

u=14.0 m/s

a=g= 9.8 m/s
s=h= 89.0 m
t=?
s=ut+1/2at*t
89=14*t+1/2*9.8*t*t
89=14*t+4.9*t*t
later i don't know............
sorry............

To find the time it takes for the stone to reach its maximum height, we can use the kinematic equation:

v = u + at

where:
v = final velocity (0 m/s at maximum height since the stone momentarily stops)
u = initial velocity (14.0 m/s upward)
a = acceleration (acceleration due to gravity, approximately -9.8 m/s²)
t = time (unknown)

Rearranging the equation, we have:

t = (v - u) / a

Substituting the values given:

t = (0 - 14.0) / -9.8

Calculating this expression gives:

t = -14.0 / -9.8
t ≈ 1.43 seconds

Therefore, it takes approximately 1.43 seconds for the stone to reach its maximum height.