The 1st hill of a roller coaster creates a velocity of 33 m/a for a coaster with a mass of 1475kg what is the maximum height the second hill can be for the roller coaster to be successful
To determine the maximum height of the second hill, we need to consider the conservation of energy.
At the top of the first hill, the roller coaster will have potential energy (due to its height) and kinetic energy (due to its velocity). The total energy at the top of the first hill can be calculated using the formula:
Total Energy = Potential Energy + Kinetic Energy
Potential Energy = mass * gravitational acceleration * height
Kinetic Energy = (1/2) * mass * velocity^2
Given:
mass = 1475 kg
velocity = 33 m/s
gravitational acceleration = 9.8 m/s^2
At the top of the first hill, the total energy is equal to the kinetic energy:
Total Energy = (1/2) * mass * velocity^2
Calculating the total energy:
Total Energy = (1/2) * 1475 kg * (33 m/s)^2 = 834,092.5 J
For the roller coaster to make it to the top of the second hill, it should have sufficient energy at the top of the first hill to overcome the gravitational potential energy at the top of the second hill.
At the top of the second hill, all the energy will be in the form of potential energy:
Total Energy = Potential Energy
Potential Energy = mass * gravitational acceleration * height
Since the roller coaster starts at rest at the top of the second hill, the initial velocity is zero. Therefore, the total energy at the top of the second hill is equal to the potential energy:
Total Energy = Potential Energy = mass * gravitational acceleration * height
Substituting the values:
834,092.5 J = 1475 kg * 9.8 m/s^2 * height
Solving for height:
height = 834,092.5 J / (1475 kg * 9.8 m/s^2) = 56.98 m
Therefore, the maximum height the second hill can be for the roller coaster to be successful is approximately 57 meters.