Physics

To solve this problem, we will use the principle of conservation of mechanical energy, while accounting for the energy lost due to friction.

 

Initial Energy Calculation

At the starting point (at height ), the roller coaster starts from rest, so its initial kinetic energy is zero. The total mechanical energy at the top is purely gravitational potential energy:

where:

is the mass of the roller coaster (which will cancel out in the calculation),

is the acceleration due to gravity,

is the initial height.

 

Thus:

 

Energy Lost Due to Friction

We are told that 10% of the total energy is lost due to friction. Therefore, only 90% of the initial energy remains as mechanical energy at the bottom of the hill: