Question

A stone is dropped from a height of \(45\,\text{m}\). What is the time taken to reach the ground? \((g = 10\,\text{m/s}^2)\)

• A. \(2\,\text{s}\)
• B. \(3\,\text{s}\)
• C. \(4\,\text{s}\)
• D. \(5\,\text{s}\)

Hint:

For objects dropped from rest, the time of fall depends only on height and gravity using \(t=\sqrt{2h/g}\).

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The problem asks for the duration of fall for an object starting from rest at a known height.
Step 2: Key Formula or Approach:
From the second equation of motion \(s = ut + \frac{1}{2}at^2\), with \(u = 0\) and \(s = h\), we get:
\[ h = \frac{1}{2}gt^2 \implies t = \sqrt{\frac{2h}{g}} \]
Step 3: Detailed Explanation:
Substitute the given values \(h = 45\,\text{m}\) and \(g = 10\,\text{m/s}^2\):
\[ t = \sqrt{\frac{2 \times 45}{10}} \]
\[ t = \sqrt{\frac{90}{10}} \]
\[ t = \sqrt{9} \]
\[ t = 3\,\text{s} \]
Step 4: Final Answer:
The time taken for the stone to reach the ground is \(3\,\text{s}\).