A 0.50 kg pendulum is pulled back and released. When the height is 0.60 m above its equilibrium position its speed is 1.9 m/s. What is the maximum height of the pendulum?

To find the maximum height of the pendulum, we need to use the principle of conservation of mechanical energy.

The mechanical energy of the pendulum consists of its potential energy (due to its height) and its kinetic energy (due to its motion). At the maximum height, all of the kinetic energy is converted into potential energy.

Let's denote the maximum height as "H". We are given the following information:

Mass of the pendulum, m = 0.50 kg
Height above equilibrium position, h = 0.60 m
Speed at this height, v = 1.9 m/s

Using the principle of conservation of mechanical energy:

Initial total mechanical energy = Final total mechanical energy

At the starting position:
Potential energy = m * g * h1
Kinetic energy = 0 (since it is at rest)

At the maximum height:
Potential energy = m * g * H
Kinetic energy = 0 (since it comes to a stop)

Setting up the equation:

m * g * h1 = m * g * H + 0

Cancelling out the mass and gravity:
h1 = H

The height above the equilibrium position when the pendulum is pulled back and released is equal to the maximum height itself. Therefore, the maximum height of the pendulum is 0.60 m.

So, the maximum height of the pendulum is 0.60 meters.