Question

A 0.2 kg ball is dropped from a height of 10 meters. What is the velocity of the ball just before it hits the ground? (Assume \( g = 9.8 \, \text{m/s}^2 \) and neglect air resistance.)

• A. \( 14.0 \, \text{m/s} \)
• B. \( 9.8 \, \text{m/s} \)
• C. \( 20.0 \, \text{m/s} \)
• D. \( 5.0 \, \text{m/s} \)

Hint:

When an object falls freely under gravity, its velocity increases as it falls. The final velocity can be found using the equation \( v = \sqrt{2gh} \) for an object dropped from rest.

Answer 1

The Correct Option is A

Using the equation of motion for an object in free fall: \[ v^2 = u^2 + 2gh \] Where: - \( u = 0 \, \text{m/s} \) (initial velocity, as the ball is dropped), - \( g = 9.8 \, \text{m/s}^2 \) is the acceleration due to gravity, - \( h = 10 \, \text{m} \) is the height from which the ball is dropped. Substitute the values: \[ v^2 = 0 + 2 \times 9.8 \times 10 = 196 \] \[ v = \sqrt{196} = 14.0 \, \text{m/s} \] Thus, the velocity of the ball just before it hits the ground is \( 14.0 \, \text{m/s} \).