Final answer:
The speed of the roller coaster at the lowest point B can be found using the principle of conservation of energy. By equating the gravitational potential energy at point A to the kinetic energy at point B, we can solve for the velocity. The velocity at the lowest point B is approximately 19.8 m/s.
Step-by-step explanation:
In order to find the speed of the roller coaster at the lowest point B, we can use the principle of conservation of energy. At point A, the roller coaster starts from rest, so its initial kinetic energy is zero. The only form of energy it has is gravitational potential energy, which is given by the equation PE = mgh, where PE is the potential energy, m is the mass, g is the acceleration due to gravity, and h is the height. At point B, all of the potential energy is converted into kinetic energy, so we can equate the two equations: mgh = 1/2 mv^2, where m is the mass, g is the acceleration due to gravity, h is the initial height, and v is the velocity at point B.
To solve for v, we can cancel out the m and g terms, resulting in v^2 = 2gh. Plugging in the values, we have v^2 = 2(9.8 m/s^2)(20 m), which simplifies to v^2 = 392 m^2/s^2. Taking the square root of both sides, we find that the velocity of the roller coaster at the lowest point B is approximately 19.8 m/s.