Final answer:
The maximum velocity of a roller coaster reaching the bottom of an 83-meter drop, assuming no friction, is calculated using the conservation of energy, resulting in a maximum velocity of approximately 40.33 m/s. Option a is the answer.
Step-by-step explanation:
To find the maximum velocity of a roller coaster when it reaches the bottom of an 83-meter drop, you can use conservation of energy assuming no work is done by friction. The potential energy at the top is converted into kinetic energy at the bottom.
The potential energy (PE) at the top is given by PE = mgh, where m is mass, g is the acceleration due to gravity (9.81 m/s2), and h is the height of the drop.
The kinetic energy (KE) at the bottom is given by KE = 1/2 m v2, where v is the velocity.
Equating the potential energy at the top to the kinetic energy at the bottom, you get mgh = 1/2 m v2.
Solving for v, the equation simplifies to v = √(2gh), and plugging in the values (g = 9.81 m/s2, h = 83 m) gives you the maximum velocity at the bottom.
Using this approach, v = √(2 * 9.81 m/s2 * 83 m) ≈ 40.33 m/s, which corresponds to answer choice A.