Final answer:
Using the principle of conservation of mechanical energy, we can determine the speed of the roller coaster at the top of an identical hill. The roller coaster starts with a speed of 6.0 m/s at the top of the drop and reaches a speed of 50.3 m/s at the bottom. By equating the initial kinetic energy to the final kinetic energy, we find that the roller coaster would attain a speed of 2.45 m/s when it reaches the top of the identical hill.
Step-by-step explanation:
To find the speed of the roller coaster when it reaches the top of the identical hill, we can use the principle of conservation of mechanical energy. The roller coaster starts at the top of the drop with a kinetic energy equal to its initial speed, which is 6.0 m/s, and potential energy equal to its height above the ground. When it reaches the bottom, its kinetic energy is given by its speed of 50.3 m/s. Since friction and air resistance are absent, the mechanical energy is conserved. Therefore, we can equate the initial kinetic energy to the final kinetic energy.
Using the equation for kinetic energy, KE = 0.5 * mass * velocity^2, we can set up the following equation:
0.5 * mass * (6.0 m/s)^2 = 0.5 * mass * (v^2), where v is the speed of the roller coaster at the top of the identical hill.
Cancelling the mass and simplifying the equation, we get:
6.0 m/s^2 = v^2
Taking the square root of both sides, we find:
v = 2.45 m/s
Therefore, the roller coaster would attain a speed of 2.45 m/s when it reaches the top of the identical hill.