Question

A ball is dropped from a height of 20 m. What is its velocity just before hitting the ground? (Take \( g = 9.8 \, \text{m/s}^2 \))

• A. \( 10 \, \text{m/s} \)
• B. \( 14 \, \text{m/s} \)
• C. \( 20 \, \text{m/s} \)
• D. \( 18 \, \text{m/s} \)

Hint:

Remember: For free fall, use the equation \( v^2 = u^2 + 2gh \), where \( u = 0 \) for an object dropped from rest.

Answer 1

The Correct Option is B

Step 1: Use the equation of motion for velocity
The equation for the velocity of an object falling freely from a height is given by: \[ v^2 = u^2 + 2gh \] where:
- \( v \) is the final velocity,
- \( u \) is the initial velocity (which is 0 for free fall),
- \( g \) is the acceleration due to gravity,
- \( h \) is the height from which the object is dropped.
Step 2: Substitute the given values Given:
- Initial velocity \( u = 0 \, \text{m/s} \),
- \( g = 9.8 \, \text{m/s}^2 \),
- Height \( h = 20 \, \text{m} \).
Substitute these values into the equation: \[ v^2 = 0 + 2 \times 9.8 \times 20 = 392 \] \[ v = \sqrt{392} \approx 14 \, \text{m/s} \] Answer: Therefore, the velocity of the ball just before hitting the ground is \( 14 \, \text{m/s} \). So, the correct answer is option (2).