You are at the park. You are going to analyze a roller coaster. You ask the attendant for the height of the first hill and find out that it is 106.1 feet tall. Along with your group members, you pace off a train waiting to be loaded. The train is 10.5 paces long. Your group then watches the roller coaster, measuring the amount of time it takes for the train to pass a single point at the bottom of the first hill. You collect the following data:

First timing: 0.42 seconds
Second timing: 0.41 seconds
Third timing: 0.46 seconds
You also determine that the track makes a 27 degree angle with the ground on the section where the train is being towed up to the top of the first hill.
With all of this information you should now be able to answer the following questions.
1) What is the speed of the train at the bottom of the first hill?
2) If you were riding on the train, how much kinetic energy would you have at the bottom of the first hill?
3) How much potential energy did you have at the top of the first hill?
4) How much energy was lost due to friction as you came down to the bottom of the first hill?
5) Finally, what is the minimum force that must have been exerted on you to pull you up to the top of the first hill?

Please help me. im soo confused!

*update

i found the speed. it was 23.5 m/s
so with this i could find #1,2 and 3.
But I still need help with #4 and 5!

To answer these questions, we need to use the principles of physics, specifically those related to energy and motion. Let's break down each question step by step:

1) To find the speed of the train at the bottom of the first hill, we can use the concept of conservation of energy. At the top of the hill, all the potential energy is converted into kinetic energy.

Potential Energy (PE) at the top = Kinetic Energy (KE) at the bottom

The potential energy at the top of the hill can be calculated using the formula:

PE = m * g * h

where m is the mass of the train, g is the acceleration due to gravity (approximately 9.8 m/s²), and h is the height of the first hill (106.1 feet).

2) If you were riding on the train, the kinetic energy you would have at the bottom of the first hill can be calculated using the equation:

KE = (1/2) * m * v^2

where m is your mass (assuming it's the same as the train's mass) and v is the velocity/speed of the train at the bottom of the first hill.

3) The potential energy you had at the top of the first hill can be calculated using the same formula as in question 1:

PE = m * g * h

4) The energy lost due to friction can be calculated by subtracting the total energy at the top of the first hill (potential energy) from the total energy at the bottom of the first hill (kinetic energy).

Energy lost due to friction = Potential Energy at the top - Kinetic Energy at the bottom

5) The minimum force exerted on you to pull you up to the top of the first hill can be calculated using the equation:

Force = mass * acceleration

where mass is your mass (assuming it's the same as the train's mass) and acceleration is the acceleration due to gravity (9.8 m/s²) plus any additional acceleration caused by the roller coaster.

Remember that these calculations use approximate values and certain assumptions to simplify the problem. Also, be sure to convert any units to a consistent system (e.g., feet to meters).

Using the given data, you should be able to plug in the values into the respective equations and calculate the answers to each question.