A 10 kg object is dropped from a height of 20 m. What is its speed just before i

A 10 kg object is dropped from a height of 20 m. What is its speed just before it hits the ground? (g = 9.8 m/s²)

A 10 kg object is dropped from a height of 20 m. What is its speed just before it hits the ground? (g = 9.8 m/s²)

Correct Answer: 19.8 m/s

Step 1: Identify the mass of the object, which is 10 kg.
Step 2: Identify the height from which the object is dropped, which is 20 m.
Step 3: Identify the acceleration due to gravity, which is 9.8 m/s².
Step 4: Use the formula for potential energy (PE) at the height: PE = mgh, where m is mass, g is gravity, and h is height.
Step 5: Calculate the potential energy: PE = 10 kg × 9.8 m/s² × 20 m.
Step 6: Use the formula for kinetic energy (KE) just before hitting the ground: KE = 0.5mv².
Step 7: Set the potential energy equal to the kinetic energy: mgh = 0.5mv².
Step 8: Cancel the mass (m) from both sides of the equation since it is the same on both sides.
Step 9: Rearrange the equation to solve for v: v² = 2gh.
Step 10: Substitute the values of g and h into the equation: v² = 2 × 9.8 m/s² × 20 m.
Step 11: Calculate the value: v² = 392 m²/s².
Step 12: Take the square root to find v: v = √392 m²/s².
Step 13: Calculate the final speed: v ≈ 19.8 m/s.

Conservation of Energy – The principle that the total energy in a closed system remains constant, allowing potential energy to convert into kinetic energy.
Kinematic Equations – Equations that describe the motion of objects under constant acceleration, particularly useful for calculating final velocities.
Gravitational Potential Energy – The energy an object possesses due to its height above the ground, calculated as mgh.
Kinetic Energy – The energy an object has due to its motion, calculated as 0.5mv².