Final answer:
The speed of the roller coaster at the bottom of the drop is found using conservation of energy principles and is calculated to be approximately 53.7 m/s, which corresponds to option (b).
Step-by-step explanation:
To solve the mathematical problem completely and find the speed of the roller coaster at the bottom of a 147-meter vertical drop, we can use the conservation of energy principle. The potential energy (PE) at the top will convert into kinetic energy (KE) at the bottom since friction is neglected. The potential energy can be calculated using PE = mgh, where m is the mass, g is the acceleration due to gravity, typically 9.81 m/s2, and h is the height.
At the bottom of the drop, all PE will have converted to KE, which is calculated using the formula KE = 0.5mv2, where v is the final velocity. Setting the initial PE equal to the final KE and cancelling out the mass since it appears on both sides of the equation, we get mgh = 0.5mv2. From this relationship, we can solve for v:
v = sqrt(2gh). Substituting the given values, we get:
v = sqrt(2 * 9.81 m/s2 * 147 m),
v = sqrt(2 * 9.81 * 147),
v = sqrt(2885.34),
v ≈ 53.7 m/s.
The correct answer is therefore option (b) 53.7 m/s.