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)
Practice Questions
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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)
10 m/s
15 m/s
20 m/s
25 m/s
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.
Questions & Step-by-step Solutions
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Q
Q: 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)
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.
Steps: 10
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.
