A person standing at the edge of a seaside cliff kicks a stone over the edge with a speed of vi = 11 m/s. The cliff is h = 55 m above the water's surface, as shown below.

How long does it take for the stone to fall to the water?

The initial speed, which is horizontal, does not matter. You only need to solve the equation for vertical motion.

55 m = (g/2) t^2 = 4.9 t^2

To find the time it takes for the stone to fall to the water, we can use the equation of motion for vertically falling objects:

h = (1/2) * g * t^2

Where:
h = height or distance fallen (55 m)
g = acceleration due to gravity (9.8 m/s^2)
t = time

To solve for t, we can rearrange the formula:

t = sqrt((2 * h) / g)

Plugging in the values:

t = sqrt((2 * 55) / 9.8)
t ≈ sqrt(11.22)
t ≈ 3.35 seconds

Therefore, it takes approximately 3.35 seconds for the stone to fall to the water.