Final answer:
To calculate the potential energy relative to the ground, use the formula PE = mgh where m is the mass of the roller coaster, g is the acceleration due to gravity, and h is the height. To find the kinetic energy, use the formula KE = (1/2)mv^2. To calculate the speed at point B, use the conservation of mechanical energy and set PE = KE.
Step-by-step explanation:
To calculate the potential energy relative to the ground, we can use the equation for gravitational potential energy, which is given by PE = mgh. In this case, the mass (m) of the roller coaster is 4 * 10^4 kg, the acceleration due to gravity (g) is 9.8 m/s^2, and the height (h) is the elevation of the roller coaster relative to the ground. plugging in these values, we can calculate the potential energy.
To find the kinetic energy, we can use the equation KE = (1/2)mv^2, where v is the speed of the roller coaster. Since the roller coaster starts at rest, the initial kinetic energy is zero.
To calculate the speed at point B, we can use the conservation of mechanical energy. The loss of gravitational potential energy is equal to the gain in kinetic energy, so we can set PE = KE and solve for the speed (v).