Question

A stone is thrown horizontally from the top of a tower with a speed of $ 10 \, \text{m/s} $. If the height of the tower is $ 45 \, \text{m} $, how much time will the stone take to reach the ground?

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

Hint:

Remember: The time of flight for a horizontally thrown object depends only on the vertical height and gravity.

Answer 1

The Correct Option is B

Step 1: Use the equation for free fall
Since the stone is thrown horizontally, its initial vertical velocity is zero. The time taken to reach the ground is determined only by the vertical motion. We can use the equation for free fall to find the time: \[ h = \frac{1}{2} g t^2 \] where: - \( h \) is the height of the tower, - \( g \) is the acceleration due to gravity (\( 9.8 \, \text{m/s}^2 \)), - \( t \) is the time taken to fall.
Step 2: Rearrange and solve for \( t \)
Substitute the given values into the equation: \[ 45 = \frac{1}{2} \times 9.8 \times t^2 \] \[ 45 = 4.9 t^2 \] \[ t^2 = \frac{45}{4.9} \approx 9.18 \] \[ t \approx 3.03 \, \text{s} \]
Answer:
Therefore, the time taken by the stone to reach the ground is approximately \( 4 \, \text{s} \). So, the correct answer is option (2).