Question

A body of mass $ 1.5 \, \text{kg} $ is dropped from a height of $ 20 \, \text{m} $. What is its speed just before hitting the ground? (Assume $ g = 9.8 \, \text{m/s}^2 $)

• A. \( 19.8 \, \text{m/s} \)
• B. \( 14 \, \text{m/s} \)
• C. \( 20 \, \text{m/s} \)
• D. \( 9.8 \, \text{m/s} \)

Hint:

Remember: When an object is dropped from a height, its initial velocity is zero, and its final velocity depends only on the height and gravity.

Answer 1

The Correct Option is A

Step 1: Use the equation for final velocity in free fall
For an object dropped from a height, the final velocity \( v \) just before hitting the ground can be calculated using the equation: \[ v = \sqrt{2gh} \] where: - \( g \) is the acceleration due to gravity, - \( h \) is the height from which the object is dropped.
Step 2: Substitute the given values
Given: - \( g = 9.8 \, \text{m/s}^2 \) - \( h = 20 \, \text{m} \) \[ v = \sqrt{2 \times 9.8 \times 20} = \sqrt{392} \approx 19.8 \, \text{m/s} \]
Answer:
Therefore, the speed of the body just before hitting the ground is \( 19.8 \, \text{m/s} \). So, the correct answer is option (1).