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Answer :
Final answer:
The roller coaster will reach a speed of approximately 39.1 m/s at the bottom of the hill, as calculated by the conversion of gravitational potential energy to kinetic energy.
Explanation:
The speed of the roller coaster when it reaches the bottom of the hill can be calculated using principles of physics, specifically the conversion of potential energy to kinetic energy. Given the roller coaster has a mass of 650 kg and the height of the hill is 78 m, the potential energy (PEg) at the top of the hill can be calculated by the formula: PEg = mgh, where 'm' is the mass, 'g' is the gravitational acceleration (9.8 m/s^2) and 'h' is the height.
The kinetic energy (KE) at the bottom of the hill, assuming no energy is lost due to air resistance or friction, will be equal to the potential energy at the top. The kinetic energy can be stated by the formula: KE = 1/2 mv^2, where 'm' is the mass and 'v' is the velocity. By setting the potential energy equal to the kinetic energy, we can solve for 'v'.
Solution:
PEg = KE => mgh = 1/2 mv^2
Solve for 'v': v = √(2gh) = √(2*9.8*78) ≈ 39.1 m/s
Learn more about Gravitational Potential energy here,
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