A roller coaster starts from rest at a height of 50 m. What is its speed at the

A roller coaster starts from rest at a height of 50 m. What is its speed at the lowest point?

A roller coaster starts from rest at a height of 50 m. What is its speed at the lowest point?

Step 1: Understand that the roller coaster starts from rest at a height of 50 meters.
Step 2: Recognize that at the top, the roller coaster has potential energy due to its height.
Step 3: Know that potential energy (PE) can be calculated using the formula PE = mgh, where m is mass, g is the acceleration due to gravity (approximately 9.8 m/s²), and h is height (50 m).
Step 4: At the lowest point, all the potential energy will have converted into kinetic energy (KE). The formula for kinetic energy is KE = 0.5mv².
Step 5: Set the potential energy equal to the kinetic energy: mgh = 0.5mv².
Step 6: Notice that the mass (m) cancels out from both sides of the equation, simplifying it to gh = 0.5v².
Step 7: Rearrange the equation to solve for v²: v² = 2gh.
Step 8: Substitute the values for g (9.8 m/s²) and h (50 m) into the equation: v² = 2 * 9.8 * 50.
Step 9: Calculate the right side: v² = 980.
Step 10: Take the square root of both sides to find v: v = sqrt(980).
Step 11: Calculate the square root to find the speed: v ≈ 31.3 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 (0.5mv^2) at the lowest point.
Gravitational Acceleration – The constant acceleration due to gravity (approximately 9.8 m/s²) that affects the motion of the roller coaster.