Final answer:
This question is about using the conservation of energy to find the height of a ski slope based on the skier's change in speed. The potential and kinetic energies at different points are equated and the equation is solved for the unknown height.
Step-by-step explanation:
The student is asking about the height of a ski slope that a skier descends from. To solve for the height of the slope, the principle of conservation of energy can be applied. This principle states that the total mechanical energy (kinetic plus potential energy) in a closed system remains constant when neglecting friction and air resistance.
According to this principle, the skier's potential energy at the top of the slope converts into kinetic energy at the bottom. The potential energy (PE) at the top is equal to mgh (where m is the mass, g is the acceleration due to gravity, and h is the height), and the kinetic energy (KE) at any point is (1/2)mv^2.
Therefore, PE at top + KE at top = KE at bottom. If we let h represent the height of the slope, we have mgh + (1/2)m(v_top)^2 = (1/2)m(v_bottom)^2. After substituting the given values and solving for h, we would find the height of the slope.
However, the actual computation has not been provided in this answer. This would normally involve substituting the given mass (100 kg), gravitational acceleration (9.81 m/s^2), initial velocity (5 m/s), and final velocity (13 m/s) into the equation and solving for h. This is a physics problem that applies the conservation of energy.