Final answer:
To calculate the speed of the rock at the vertical position of its pendulum swing, apply the conservation of energy principle, converting the initial potential energy at the maximum angle to kinetic energy at the bottom position.
Step-by-step explanation:
To find the speed of the rock when the pendulum passes through the vertical position, we can use the principles of conservation of energy. Initially, the rock has potential energy due to its height above the lowest point. As the pendulum swings down, this potential energy is converted into kinetic energy.
Using the maximum angle of 45 degrees, we can calculate the height above the lowest point using trigonometry. The difference in height (h) from the maximum angle position to the lowest point can be found using h = L(1 - cos(θ)), where L is the length of the pendulum and θ is the angle from the vertical. The potential energy at this height is mgh, where mg is the weight of the rock and g is the acceleration due to gravity.
At the vertical position, all this potential energy has been converted into kinetic energy, which is ½mv², where v is the speed. Equating the potential energy to kinetic energy, we get mgh = ½mv². Solving for v, we can calculate the speed of the rock at the vertical position.