A stone is thrown vertically upward with a speed of 10.0 m/s from the edge of a cliff 59.0 m high.

How much later does it reach the bottom of the cliff?
What is its speed just before hitting?
What total distance did it travel?

vertical position:

hf=hi+Vi*t-1/2 g t^2
you know hf=-59
hi=0 solve for t, notice it is a quadratic.

Finalspeed=Vi -g*t
Vi=10m/s

total distance=59+2*heightaboveclift

Not to figure the height above. At the top, Vf=0 (think about that).
Vf=Vi-gt solve for t at the top.
h=Vi*t-1/2 g t^2 solve for h, heightabove clift.

To find the time it takes for the stone to reach the bottom of the cliff, we need to use kinematic equations.

First, we can use the equation:
v = u + at
where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.

Since the stone is thrown vertically upward, the initial velocity (u) is +10.0 m/s and the acceleration (a) is -9.8 m/s² (negative because it's directed downwards due to gravity).

We can rearrange the equation to solve for time (t):
t = (v - u) / a

The final velocity (v) is 0 m/s because the stone reaches its highest point and then falls back down.

Substituting the values into the equation:
t = (0 - 10.0) / -9.8
t = 1.02 seconds

Therefore, it takes approximately 1.02 seconds for the stone to reach the bottom of the cliff.

To find the speed of the stone just before hitting the ground, we can use the equation:
v = u + at

Here, the initial velocity (u) is 0 m/s (at the highest point), and the acceleration (a) is +9.8 m/s² (positive because it's directed downward).

Substituting the values into the equation:
v = 0 + (9.8)(1.02)
v ≈ 10 m/s

Therefore, the speed of the stone just before hitting the ground is approximately 10 m/s.

To find the total distance traveled, we need to calculate the distance traveled upward and downward separately and then add them together.

The distance traveled upward is the height of the cliff, which is 59.0 m.

The distance traveled downward can be calculated using the equation:
s = ut + (1/2)at²

Substituting the values:
s = (0)(1.02) + (1/2)(9.8)(1.02)²
s ≈ 5.0 m

Adding the distances traveled upward and downward:
Total distance = 59.0 m + 5.0 m
Total distance ≈ 64.0 m

Therefore, the total distance traveled by the stone is approximately 64.0 meters.