At the top of the Washington monument, a bird drops an acorn into the reflecting pool 169m below. If the acorn has a massof 1.0 kg, with what velocity would it hit the water?

v=sqrt(2gh)

To determine the velocity at which the acorn hits the water, we can use the principle of conservation of energy. The potential energy of the acorn at the top of the Washington Monument will be converted to kinetic energy as it falls. Assuming no other forces are acting on the acorn (such as air resistance), we can equate these two energies:

Potential Energy at the top = Kinetic Energy at impact

The potential energy of an object is given by the equation:

Potential Energy = mass * gravity * height

Where:
- mass = 1.0 kg (mass of the acorn)
- gravity = 9.8 m/s^2 (acceleration due to gravity on Earth)
- height = 169 m (height from the top of the Washington Monument to the surface of the reflecting pool)

Kinetic energy is given by the equation:

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

Where:
- mass = 1.0 kg (mass of the acorn)
- velocity = unknown (velocity at impact)

Now, we can equate the two energies:

mass * gravity * height = (1/2) * mass * velocity^2

Simplifying the equation by canceling the mass term on both sides:

gravity * height = (1/2) * velocity^2

Solving for velocity:

velocity^2 = (2 * gravity * height)

velocity = √(2 * gravity * height)

Now, let's substitute the known values into the equation and calculate the velocity:

velocity = √(2 * 9.8 m/s^2 * 169 m)