A person standing at the edge of a seaside cliff kicks a stone over the edge with a speed of 18 m/s. The cliff is 52 m above the water's surface. How long does it take for the stone to fall to the water? With what speed does it strike the water?
3.3
Why did the stone go to the water? Because it couldn't handle the pressure of living on the edge! Now let's calculate its fall, shall we?
Using the formula s = ut + 0.5gt², where s is the distance, u is the initial velocity, t is the time, and g is the acceleration due to gravity, we can plug in the values.
Since the stone is kicked over the edge, its initial velocity, u, is 18 m/s. The acceleration due to gravity, g, is approximately 9.8 m/s² (let's not get too heavy about it). The distance, s, is the height of the cliff, which is 52 m.
Now we want to find the time it takes for the stone to fall to the water, so let's rearrange the formula to solve for t: t = √(2s/g).
Plugging in the values, we get:
t = √(2 * 52 m / 9.8 m/s²)
t ≈ √(10.6122)
t ≈ 3.26 seconds (approximately)
So, it will take around 3.26 seconds for the stone to fall to the water. But what about the speed it strikes the water with? Well, when the stone reaches the water, its vertical speed will be the same as the final speed it achieved during its acceleration due to gravity.
Using the equation v = u + gt, where v is the final velocity, we can calculate it:
v = 18 m/s + (9.8 m/s² * 3.26 seconds)
v ≈ 18 m/s + 31.948 m/s
v ≈ 49.948 m/s
So, the stone will strike the water at a speed of approximately 49.948 m/s. Just remember, it's all water under the bridge (or shall I say, cliff)!
To find the time it takes for the stone to fall to the water and the speed with which it strikes the water, we can use the principles of kinematics. There are a few equations we can use to solve this.
First, we'll use the equation for the time it takes an object to fall freely from a given height:
h = (1/2) * g * t^2
where h is the height, g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time.
Rearranging the equation to solve for t, we get:
t^2 = (2 * h) / g
Next, we'll use the equation for the final velocity of a freely falling object:
v = g * t
where v is the final velocity of the object.
Now, let's substitute the given values into the equations:
h = 52 m
g = 9.8 m/s^2
Plugging these values into the equation for time:
t^2 = (2 * 52 m) / (9.8 m/s^2)
t^2 = 10.6122 s^2
Taking the square root of both sides, we find:
t ≈ 3.26 s
So, it takes approximately 3.26 seconds for the stone to fall to the water.
To calculate the speed at which it strikes the water, we can use:
v = g * t
Plugging in the values:
v = 9.8 m/s^2 * 3.26 s
v ≈ 31.948 m/s
So, the stone strikes the water with a speed of approximately 31.948 m/s.