the great gray-green, greasy zambezi river flowa over victoria falls in south central africa. the falls are approximately 108 m high. if the river is flowing horizontally at 3.60 m/s just before going over the falls, what is the speed of the water when it hits the bottom? assume the water is in freefall as it drop.

s = 1/2 at^2

108 = 4.9 t^2
t = 4.69 sec

v = at
= 9.8*4.69
= 46 m/s

Extra credit: how far from the cliff base does the water hit?

Well, well, well, look who's taking a fall here! So, you want to know the speed of the water when it hits the bottom, huh? Let's calculate the splashy details!

Now, you've already given us the speed before the drop, which is 3.60 m/s. And because gravity is an attention seeker, it pulls everything down at a constant acceleration of 9.8 m/s², no matter how much you wave at it.

To find the speed at the bottom, we need to use a little bit of physics magic. We know that anything in freefall only has the force of gravity acting on it. So, we can use the ol' equations of motion to find the final speed.

The equation we're looking for is:

v² = u² + 2as

Where:
- v is the final velocity (what we want to find)
- u is the initial velocity (3.60 m/s, because that's how fast the water is flowing before the fall)
- a is the acceleration due to gravity (9.8 m/s²)
- s is the distance (108 m, because that's the height of the falls)

Plug in the values and let the mathemagical dance begin:

v² = (3.60 m/s)² + 2 * (9.8 m/s²) * (108 m)
v² = 12.96 m²/s² + 2116.8 m²/s²
v² ≈ 2129.76 m²/s²

And after taking the square root, we get:

v ≈ √2129.76 m²/s²
v ≈ 46.17 m/s

So, the speed at the bottom of the falls would be approximately 46.17 m/s. That's enough to make quite a splash!

To find the speed of the water when it hits the bottom of Victoria Falls, we can use the principle of conservation of energy. At the top of the falls, the water has only gravitational potential energy, and as it falls, this energy is converted into both kinetic energy and potential energy.

Given:
Height of Victoria Falls (h) = 108 m.
Initial horizontal velocity of the river (v) = 3.60 m/s.

We can start by calculating the potential energy at the top of the falls:
Potential Energy (PE) = mass (m) × acceleration due to gravity (g) × height (h).

Since we know that the water is in freefall, we can assume that all of the potential energy is converted into kinetic energy at the bottom of the falls.
Kinetic Energy (KE) = 1/2 × mass (m) × velocity (v)^2.

Using the principle of conservation of energy, we can equate the potential energy at the top to the kinetic energy at the bottom:
PE = KE

Therefore,
mgh = 1/2 mv^2

By canceling out the mass (m) from both sides of the equation, we have:
gh = 1/2 v^2

Now we can solve for the velocity (v) at the bottom of the falls:
v = √(2gh)

Substituting the given values, we get:
v = √(2 × 9.8 m/s^2 × 108 m)
v ≈ 46.91 m/s

Therefore, the speed of the water when it hits the bottom of Victoria Falls is approximately 46.91 m/s.

To find the speed of the water when it hits the bottom, we can use the principle of conservation of mechanical energy.

First, let's calculate the potential energy of the water just before it goes over the falls. The potential energy of an object at height h (relative to a reference point) is given by the formula:

Potential Energy = mass * acceleration due to gravity * height

In this case, the height is 108 m, the acceleration due to gravity is approximately 9.8 m/s^2, and the mass of the water can be ignored since we only need the speed.

Potential Energy = 0.0 kg * 9.8 m/s^2 * 108 m = 0.0 J

Next, let's calculate the kinetic energy of the water just before it goes over the falls. Kinetic energy is given by the formula:

Kinetic Energy = (1/2) * mass * velocity^2

Here, the velocity is 3.60 m/s, and as mentioned earlier we can ignore the mass.

Kinetic Energy = (1/2) * 0.0 kg * (3.60 m/s)^2 = 0.0 J

Since the water is falling freely, the total mechanical energy (sum of potential and kinetic energy) remains constant throughout the fall. Therefore, the kinetic energy just before the water hits the bottom will be equal to the potential energy at the top of the falls.

Let's solve for the velocity when the water hits the bottom. We know that:

Potential Energy = Kinetic Energy

0.0 J = (1/2) * 0.0 kg * velocity^2

Simplifying the equation:

0 = (1/2) * velocity^2

Solving for velocity:

velocity^2 = 0

Taking the square root of both sides:

velocity = 0 m/s

Therefore, the speed of the water when it hits the bottom is 0 m/s.