A ball is thrown horizontally with a speed of `20 m//s` from the top of a tower of height 100m
Time taken by the ball to strike the ground is

Options

A. `sqrt20s`
B. `2 sqrt20 s`
C. `4 sqrt20 s`
D. `10s`

Explanation

To find the time taken by the ball to strike the ground when thrown horizontally from a height of 100 meters, we can use the equations of motion. Here’s a step-by-step solution:

### Step 1: Identify the parameters
- Height of the tower (h) = 100 m
- Initial vertical velocity (u_y) = 0 m/s (since the ball is thrown horizontally)
- Acceleration due to gravity (g) = 10 m/s² (approximately)

### Step 2: Use the equation of motion
We can use the second equation of motion for vertical motion:
\[ s_y = u_y t + \frac{1}{2} g t^2 \]
where:
- \( s_y \) is the vertical displacement (which is -100 m, since it falls down),
- \( u_y \) is the initial vertical velocity (0 m/s),
- \( g \) is the acceleration due to gravity (10 m/s²),
- \( t \) is the time taken to fall.

### Step 3: Substitute the values
Substituting the known values into the equation:
\[ -100 = 0 \cdot t + \frac{1}{2} \cdot 10 \cdot t^2 \]

This simplifies to:
\[ -100 = 5t^2 \]

### Step 4: Solve for t²
Rearranging the equation gives:
\[ t^2 = \frac{-100}{5} \]
\[ t^2 = 20 \]

### Step 5: Solve for t
Taking the square root of both sides:
\[ t = \sqrt{20} \]
\[ t \approx 4.47 \text{ seconds} \]

### Final Answer
The time taken by the ball to strike the ground is approximately **4.47 seconds**.

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