Question

A stone is dropped from a height of \(20\,\text{m}\); calculate its velocity just before it hits the ground \((g = 10\,\text{m/s}^2)\).

• A. \(10\,\text{m/s}\)
• B. \(15\,\text{m/s}\)
• C. \(20\,\text{m/s}\)
• D. \(25\,\text{m/s}\)

Hint:

When an object is dropped freely, the initial velocity \(u = 0\). Use the equation \(v^2 = 2gh\) to quickly find the final velocity.

Answer 1

The Correct Option is C

Concept: For motion under gravity with constant acceleration, we use the kinematic equation: \[ v^2 = u^2 + 2gh \] where
• \(u\) = initial velocity
• \(v\) = final velocity
• \(g\) = acceleration due to gravity
• \(h\) = height fallen

Step 1: Identify the given quantities. Since the stone is dropped: \[ u = 0 \] \[ g = 10\,\text{m/s}^2 \] \[ h = 20\,\text{m} \]

Step 2: Substitute into the kinematic equation. \[ v^2 = 0 + 2(10)(20) \] \[ v^2 = 400 \]

Step 3: Find the velocity. \[ v = \sqrt{400} \] \[ v = 20\,\text{m/s} \] Thus the velocity just before hitting the ground is \[ \boxed{20\,\text{m/s}} \]