Final answer:
To determine the velocity of the roller coaster at the top of the loop, we can use the principles of conservation of mechanical energy. By equating the potential energy to the kinetic energy, we can calculate the velocity using the equations for potential and kinetic energy.
Step-by-step explanation:
In this situation, we are trying to determine the velocity of the roller coaster at the top of the loop. To solve this, we can use the principle of conservation of mechanical energy. At the top of the loop, the roller coaster will have both potential energy and kinetic energy. The potential energy will be at its maximum, while the kinetic energy will be at its minimum.
Using the conservation of energy, we can equate the potential energy at the top of the loop to the kinetic energy at that point. The equation for potential energy is PE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height of the loop.
By equating the potential energy to the kinetic energy, we can find the velocity of the roller coaster at the top of the loop. The equation for kinetic energy is KE = 1/2 mv^2, where m is the mass and v is the velocity.