At six flags great adventure amusment park in new jersy, a popular ride known as "free fall" carries passangers up to a height of 33.5 m and drops them to the ground inside a small cage. How fast are the passengers going at the bottom of this eshilirating journey?
Vf^2= 2*g*height
2.3
To determine the speed of the passengers at the bottom of the "free fall" ride, we can use the principles of conservation of energy. At the top of the ride, the potential energy of the passengers is at its maximum, and at the bottom, it is converted into kinetic energy.
First, let's calculate the potential energy at the top of the ride using the formula:
Potential Energy (PE) = Mass (m) * Acceleration due to gravity (g) * Height (h)
The mass and acceleration due to gravity are constant, so we can disregard them for now. The potential energy at the top of the ride is:
PE_top = 0.5 * 9.8 m/s^2 * 33.5 m
Next, we can equate this potential energy to the kinetic energy at the bottom of the ride (assuming negligible air resistance):
Potential Energy (PE_top) = Kinetic Energy (KE_bottom)
0.5 * 9.8 m/s^2 * 33.5 m = 0.5 * mass * velocity^2
Simplifying the equation:
33.5 * 9.8 = 0.5 * velocity^2
Now, solve for velocity:
velocity = √((33.5 * 9.8) / 0.5)
Plugging in the values and solving the equation:
velocity ≈ √(328.3) ≈ 18.1 m/s
Therefore, the passengers are traveling at approximately 18.1 meters per second at the bottom of the "free fall" ride in Six Flags Great Adventure Amusement Park in New Jersey.