Final answer:
The skater's kinetic energy at the bottom of the ramp is found by using the conservation of energy principle, which in the absence of friction, equates potential energy at the top with kinetic energy at the bottom, yielding 14,112 joules.
Step-by-step explanation:
To solve for the kinetic energy of the skater at the bottom of the ramp, we can use the principle of conservation of energy. This principle states that if there's no friction, the potential energy at the top of the ramp will be converted entirely into kinetic energy at the bottom of the ramp. The formula for gravitational potential energy (PE) is PE = m * g * h, where m is mass, g is the acceleration due to gravity (9.8 m/s2), and h is height.
Plugging in the given values:
- Mass (m) = 72 kg
- Height (h) = 20 m
- Gravitational acceleration (g) = 9.8 m/s2
The potential energy at the top is PE = 72 kg * 9.8 m/s2 * 20 m, which simplifies to PE = 14,112 J (joules). Since there is no friction, this will equal the kinetic energy at the bottom of the ramp.
Therefore, the correct answer is a) 14,112 J, as this is the amount of kinetic energy the skater will have at the bottom of the ramp.