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: Apply the free fall final velocity equation
For an object released from rest at a certain height, its final velocity \( v \) immediately prior to impact is determined by the equation:\[v = \sqrt{2gh}\]With:- \( g \) representing the acceleration due to gravity,- \( h \) indicating the initial drop height.
Step 2: Input the provided data
Provided values:- \( g = 9.8 \, \text{m/s}^2 \) - \( h = 20 \, \text{m} \)Calculating the velocity:\[v = \sqrt{2 \times 9.8 \times 20} = \sqrt{392} \approx 19.8 \, \text{m/s}\]
Conclusion:
Consequently, the object's speed just before impact is \( 19.8 \, \text{m/s} \). This corresponds to option (1).