Lora (of mass 42.8 kg) is an expert skier. She

starts at 2.3 m/s at the top of the lynx run,
which is 114 m above the bottom.
What is her final kinetic energy at the bottom of the ski run?
Answer in units of J

To calculate Lora's final kinetic energy at the bottom of the ski run, we can use the conservation of energy principle. The initial potential energy at the top of the run is equal to the final kinetic energy at the bottom of the run.

The potential energy (PE) can be calculated using the formula:

PE = mass * gravitational acceleration * height

Where:
- mass = 42.8 kg (Lora's mass)
- gravitational acceleration = 9.8 m/s^2 (acceleration due to gravity)
- height = 114 m (height of the ski run)

PE = 42.8 kg * 9.8 m/s^2 * 114 m
PE = 48,205.6 J

Since the potential energy is equal to the kinetic energy at the bottom of the run:

KE = PE

Therefore, Lora's final kinetic energy at the bottom of the ski run is 48,205.6 J.

To find Lora's final kinetic energy at the bottom of the ski run, we need to use the principle of conservation of energy, which states that the total mechanical energy of a system remains constant if no external forces are acting on it.

The total mechanical energy of a system is the sum of its kinetic energy and potential energy. At the top of the ski run, Lora has both kinetic energy and potential energy. Her initial kinetic energy can be calculated using the formula:

Initial Kinetic Energy = (1/2) * mass * velocity^2

Given that Lora's mass is 42.8 kg and her initial velocity is 2.3 m/s, we can calculate her initial kinetic energy:

Initial Kinetic Energy = (1/2) * 42.8 kg * (2.3 m/s)^2

Next, we find Lora's initial potential energy using the formula:

Initial Potential Energy = mass * gravity * height

The mass and height are given as 42.8 kg and 114 m, respectively. The acceleration due to gravity is approximately 9.8 m/s^2. Substituting the values into the formula, we get:

Initial Potential Energy = 42.8 kg * 9.8 m/s^2 * 114 m

Now, to find Lora's final kinetic energy at the bottom of the ski run, we need to subtract the initial potential energy from the total mechanical energy. Since the mechanical energy is conserved, we'll have:

Final Kinetic Energy = Total Mechanical Energy - Initial Potential Energy

Finally, we can calculate Lora's final kinetic energy:

Final Kinetic Energy = Initial Kinetic Energy - Initial Potential Energy

Plug in the calculated values and perform the subtraction to get the final answer in joules (J).

V^2 = (2.3)^2 + 19.6*114 = 2239.69

V = 47.3 m/s. = Final velocity.

Ek=0.5m*V^2=0.5*42.8*(47.3)^2=47,929 J.