a person standing at the edge of a seaside cliff kicks a stone over the edge with a speed of 18 ms. The cliff is 52m above the waters surface. How long does it take for the stone to fall to the water? With what speed does it strike the water?

Since the stone start with no initial vertical velocity component, the time T to hit the water is given by

H = 52 m = (1/2) g T^2
which leads to
T = sqrt(2H/g)

The speed V2 when it hits the surface is most easily computed using energy conservation.

(1/2) m V2^2 = (1/2) m V1^2 + m g H
V2^2 = V1^2 + 2gH

V1 is the initial velocity, 18 m/s.
You know what g is, I assume.

To find out how long it takes for the stone to fall to the water, we can use the equation of motion. The equation is given by:

s = ut + (1/2)gt^2

Where:
s = initial height = 52 m
u = initial velocity = 18 m/s (upward)
g = acceleration due to gravity = 9.8 m/s^2 (downward)
t = time taken to fall

To find the time taken to fall, we need to rearrange the equation as follows:

s = ut + (1/2)gt^2
0 = ut + (1/2)gt^2 - s
0 = (1/2)gt^2 + ut - s

Substituting the given values into the equation:

0 = (1/2)(9.8)t^2 + 18t - 52

We can now solve this quadratic equation to find the value of t.

Using either factoring, completing the square, or the quadratic formula, the equation can be solved to find t ≈ 3.36 seconds (rounded to two decimal places).

Now, to find the speed with which the stone strikes the water, we can use the equation of motion:

v = u + gt

Where:
v = final velocity (speed) = ?
u = initial velocity = 18 m/s (upward)
g = acceleration due to gravity = 9.8 m/s^2 (downward)
t = time taken to fall = 3.36 seconds

Substituting the given values into the equation:

v = 18 + (9.8)(3.36)
v = 18 + 33.03
v ≈ 51.03 m/s (rounded to two decimal places)

Therefore, it takes approximately 3.36 seconds for the stone to fall to the water, and it strikes the water with a speed of approximately 51.03 m/s.

To calculate the time it takes for the stone to fall to the water and the speed at which it strikes the water, we can use the equations of motion.

First, let's find the time it takes for the stone to fall to the water. We can use the equation:

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

Where:
- h is the vertical distance traveled (52m in this case)
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
- t is the time taken

Rearranging the equation to solve for time (t), we have:

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

Substituting the given values, we have:

t = sqrt((2 * 52) / 9.8)
t = sqrt(104 / 9.8)
t ≈ 4.15 seconds

Therefore, it takes approximately 4.15 seconds for the stone to fall to the water.

Next, let's calculate the speed at which the stone strikes the water. We can use the equation:

v = g * t

Where:
- v is the final velocity (speed) of the stone
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
- t is the time taken (which we found to be approximately 4.15 seconds)

Substituting the values, we have:

v = 9.8 * 4.15
v ≈ 40.67 m/s

Therefore, the stone will strike the water with a speed of approximately 40.67 m/s.

e=mc^2