Final answer:
To find the speed of the roller coaster when it reaches the ground level, we can use the principle of conservation of energy. The roller coaster starts at a height of 71.6 m above the ground and has no initial velocity. All of its initial potential energy is converted into kinetic energy as it falls to the ground.
Step-by-step explanation:
To find the speed of the roller coaster when it reaches the ground level, we can use the principle of conservation of energy. The roller coaster starts at a height of 71.6 m above the ground and has no initial velocity. This means that all of its initial potential energy is converted into kinetic energy as it falls to the ground.
We can calculate the potential energy at the starting point using the formula:
PE = mgh
where m is the mass (given as 850 kg in the question), g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height (71.6 m).
Next, we can use the formula for kinetic energy to calculate the speed at the ground level:
KE = (1/2)mv²
where m is the mass and v is the velocity. Since all of the initial potential energy is converted into kinetic energy, we can equate the potential energy to the kinetic energy to solve for v.
Plugging in the given values, we can solve for v:
850 * 9.8 * 71.6 = (1/2) * 850 * v²
Simplifying the equation, we get:
615720 = 425 * v²
Dividing both sides by 425 and taking the square root, we can find v:
v = √(615720/425) = 36.4 m/s
Therefore, the speed of the roller coaster when it reaches the ground level is approximately 36.4 m/s.