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. \(5\,\text{s}\) \bigskip

Hint:

For objects \textbf{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

Concept: For a body falling freely under gravity, the time taken to fall from height \(h\) is given by: :contentReference[oaicite:0]{index=0} where \begin{itemize} \item \(t\) = time of fall \item \(h\) = height \item \(g\) = acceleration due to gravity \end{itemize} Step 1: {\color{red}Substitute the given values.} \[ h = 45\,\text{m}, \quad g = 10\,\text{m/s}^2 \] \[ t = \sqrt{\frac{2 \times 45}{10}} \] Step 2: {\color{red}Simplify the expression.} \[ t = \sqrt{\frac{90}{10}} \] \[ t = \sqrt{9} \] \[ t = 3\,\text{s} \] Thus, the time taken for the stone to reach the ground is: \[ t = 3\,\text{s} \] \bigskip