Question

A stone is dropped from a height of 45 m. What is the time taken for the stone to reach the ground?

• A. 3 s
• B. 5 s
• C. 6 s
• D. 9 s

Hint:

Remember: The equation \( s = \frac{1}{2} g t^2 \) is useful for calculating the time of fall under gravity, starting from rest.

Answer 1

The Correct Option is A

Step 1: Use the equation of motion For a body dropped from rest, the equation for distance traveled under uniform acceleration due to gravity is: \[ s = \frac{1}{2} g t^2 \] where: - \( s \) is the distance traveled (45 m), - \( g \) is the acceleration due to gravity (approximately \( 9.8 \, \text{m/s}^2 \)), - \( t \) is the time taken (what we need to find). Step 2: Substitute the given values Substitute \( s = 45 \, \text{m} \) and \( g = 9.8 \, \text{m/s}^2 \) into the equation: \[ 45 = \frac{1}{2} \times 9.8 \times t^2 \] \[ 45 = 4.9 \times t^2 \] \[ t^2 = \frac{45}{4.9} = 9.18 \] \[ t = \sqrt{9.18} \approx 3 \, \text{seconds} \] Answer: Therefore, the time taken for the stone to reach the ground is approximately 3 seconds. So, the correct answer is option (1).