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

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Question: A 10 kg object is dropped from a height of 20 m. What is its speed just before it hits the ground? (Assume no air resistance)

Options:

Correct Answer: 20 m/s

Solution:

Using conservation of energy: Potential Energy = Kinetic Energy. mgh = 0.5mv². v = sqrt(2gh) = sqrt(2 × 9.8 m/s² × 20 m) = 20 m/s.

A 10 kg object is dropped from a height of 20 m. What is its speed just before it hits the ground? (Assume no air resistance)

A 10 kg object is dropped from a height of 20 m. What is its speed just before it hits the ground? (Assume no air resistance)

Step 1: Identify the mass of the object. The mass (m) is 10 kg.
Step 2: Identify the height from which the object is dropped. The height (h) is 20 m.
Step 3: Use the formula for gravitational potential energy (PE) which is PE = mgh, where g is the acceleration due to gravity (approximately 9.8 m/s²).
Step 4: Calculate the potential energy just before the object is dropped: PE = 10 kg × 9.8 m/s² × 20 m.
Step 5: Simplify the calculation: PE = 1960 Joules.
Step 6: When the object falls, this potential energy converts to kinetic energy (KE) just before it hits the ground. The formula for kinetic energy is KE = 0.5mv².
Step 7: Set the potential energy equal to the kinetic energy: 1960 Joules = 0.5 × 10 kg × v².
Step 8: Rearrange the equation to solve for v²: v² = (1960 Joules) / (0.5 × 10 kg).
Step 9: Calculate v²: v² = 1960 / 5 = 392.
Step 10: Take the square root of v² to find v: v = sqrt(392).
Step 11: Calculate the final speed: v ≈ 20 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.
Kinematics – The study of motion, specifically how objects move under the influence of forces.
Gravitational Potential Energy – The energy an object possesses due to its position in a gravitational field, calculated as mgh.
Kinetic Energy – The energy an object has due to its motion, calculated as 0.5mv².