Final answer:
The maximum height of the pendulum is calculated by using the conservation of energy principles, converting kinetic energy at the lowest point into potential energy at the maximum height. The kinetic energy is converted to potential energy to find the height, resulting in a maximum height of 0.86 m, which is option C.
Step-by-step explanation:
To find the maximum height of the pendulum, we can use the principles of conservation of energy. When the pendulum reaches the lowest point in its swing, all the potential energy has been converted into kinetic energy. The formula for kinetic energy (KE) is KE = 0.5 × m × v^2, where m is the mass of the pendulum and v is its speed at the lowest point.
Using the details that the mass of the pendulum is 2 kg and its speed at the lowest point is 4.1 m/s, we can calculate the kinetic energy:
KE = 0.5 × 2 kg × (4.1 m/s)^2
KE = 0.5 × 2 kg × 16.81 m^2/s^2
KE = 16.81 J
This kinetic energy is equal to the potential energy (PE) at the maximum height, which is given by PE = m × g × h, where g is the acceleration due to gravity (9.81 m/s^2) and h is the height. Solving for h, we have:
h = KE / (m × g)
h = 16.81 J / (2 kg × 9.81 m/s^2)
h = 16.81 J / 19.62 kg·m/s^2
h = 0.857 m
Therefore, the maximum height of the pendulum is 0.86 m, which corresponds to option C.