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A roller coaster starts from rest at a height of 30 m. What is its speed at the

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Question: A roller coaster starts from rest at a height of 30 m. What is its speed at the lowest point? (g = 9.8 m/s²)

Options:

  1. 10 m/s
  2. 15 m/s
  3. 20 m/s
  4. 25 m/s

Correct Answer: 20 m/s

Solution: 

Using conservation of energy, potential energy at the top = kinetic energy at the bottom. mgh = 0.5mv². Solving gives v = √(2gh) = √(2 * 9.8 * 30) = 24.5 m/s.

A roller coaster starts from rest at a height of 30 m. What is its speed at the

Practice Questions

Q1
A roller coaster starts from rest at a height of 30 m. What is its speed at the lowest point? (g = 9.8 m/s²)
  1. 10 m/s
  2. 15 m/s
  3. 20 m/s
  4. 25 m/s

Questions & Step-by-Step Solutions

A roller coaster starts from rest at a height of 30 m. What is its speed at the lowest point? (g = 9.8 m/s²)
  • Step 1: Understand that the roller coaster starts from a height of 30 meters and is initially at rest, meaning its initial speed is 0 m/s.
  • Step 2: Recognize that at the top of the roller coaster, it has potential energy due to its height. The formula for potential energy (PE) is PE = mgh, where m is mass, g is the acceleration due to gravity (9.8 m/s²), and h is height (30 m).
  • Step 3: At the lowest point of the roller coaster, all the potential energy will have converted into kinetic energy (KE). The formula for kinetic energy is KE = 0.5mv², where v is the speed we want to find.
  • Step 4: Set the potential energy equal to the kinetic energy: mgh = 0.5mv². Since mass (m) appears on both sides, we can cancel it out.
  • Step 5: This simplifies our equation to gh = 0.5v².
  • Step 6: Rearrange the equation to solve for v²: v² = 2gh.
  • Step 7: Substitute the values for g (9.8 m/s²) and h (30 m) into the equation: v² = 2 * 9.8 * 30.
  • Step 8: Calculate the right side: v² = 588.
  • Step 9: Take the square root of both sides to find v: v = √588.
  • Step 10: Calculate the square root to find the speed: v ≈ 24.5 m/s.
  • Conservation of Energy – The principle that energy cannot be created or destroyed, only transformed from one form to another, in this case from potential energy to kinetic energy.
  • Kinetic and Potential Energy – Understanding the relationship between potential energy (mgh) at a height and kinetic energy (0.5mv²) at the lowest point.
  • Gravitational Acceleration – The constant acceleration due to gravity (g = 9.8 m/s²) that affects the motion of the roller coaster.
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