Final answer:
The initial velocity of a roller coaster can be calculated using the kinetic energy formula, and its kinetic energy at various points can be determined by applying the principle of conservation of energy, considering the roller coaster and Earth's gravitational potential energy conversions.
Step-by-step explanation:
The student is asking about the conservation of energy in the context of a roller coaster, which is a classic physics problem.
Solution for (a):
The initial velocity of the roller coaster can be found using the kinetic energy (KE) formula: KE = 0.5 * m * v^2. Therefore, v = sqrt((2 * KE) / m), where m is the mass of the coaster (50 kg) and KE is the kinetic energy (50 J). Using the formula, the initial velocity (v) can be calculated.
Solution for (b):
When the coaster is at a point where its gravitational potential energy (GPE) is 300 J, the kinetic energy (KE) will be the total initial mechanical energy minus the new GPE, because the total energy must be conserved. This can be calculated by subtracting the new GPE from the initial total energy (450 J).
Solution for (c):
The kinetic energy (KE) at ground level will be equal to the initial total mechanical energy (sum of GPE and KE at the top of the hill) since all the GPE will have been converted to KE in the absence of friction.