Rueckert and Coco are riding a roller coaster at Six Flags. The combine mass of the guys and the coaster car is 284 kg. They are on top, motionless, of a 106 m hill. Eventually, their coaster car rushes down the hill. What is their velocity when the car is 38 m from the bottom? Assume no loss of energy due to friction.
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Explanation:
To calculate the velocity of Rueckert and Coco's coaster car when it is 38 m from the bottom of the hill, we can use the principle of conservation of energy.
At the top of the hill, all of the energy is in the form of gravitational potential energy (GPE). As the coaster car moves down, this potential energy is converted into kinetic energy (KE).
The formula for gravitational potential energy is given as:
GPE = m * g * h
Where:
m is the combined mass of Rueckert, Coco, and the coaster car (284 kg)
g is the acceleration due to gravity (approximately 9.8 m/s²)
h is the height of the hill (106 m)
At the top of the hill, GPE is maximized. As the car moves downwards, the GPE decreases while the KE increases, following the conservation of energy principle.
Let's denote the velocity of the car at 38 m from the bottom as v.
The formula for kinetic energy is given as:
KE = (1/2) * m * v²
Since there is no loss of energy due to friction, the initial GPE is equal to the final KE.
m * g * h = (1/2) * m * v²
Now, we can solve for v:
v² = 2 * g * h
v = √(2 * g * h)
Plugging in the given values:
v = √(2 * 9.8 m/s² * 106 m)
v ≈ √20840.8 m²/s²
v ≈ 144.31 m/s
Therefore, when the coaster car is 38 m from the bottom of the hill, its velocity is approximately 144.31 m/s.
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