A ball is dropped from a height of 49 m. The wind is blowing horizontally. Due to wind a constant horizontal acceleration is provided to the ball. Choose the correct statement (s).

Options

A. Path of the ball is circular one
B. Path of the ball is a curved one
C. The time taken by the ball to reach the ground is 3.16 s
D. Actual distance travelled by the ball is less than 49m

Explanation

To solve the problem step by step, we need to analyze the motion of the ball dropped from a height of 49 meters while experiencing a constant horizontal acceleration due to the wind.

### Step 1: Identify the vertical motion
The ball is dropped from a height of 49 meters. In vertical motion, the only force acting on the ball is gravity, which provides a downward acceleration of \( g = 9.8 \, \text{m/s}^2 \).

### Step 2: Use the equation of motion for vertical displacement
We can use the second equation of motion to find the time taken for the ball to reach the ground:
\[ h = ut + \frac{1}{2} a t^2 \]
Where:
- \( h = 49 \, \text{m} \) (height)
- \( u = 0 \, \text{m/s} \) (initial velocity)
- \( a = g = 9.8 \, \text{m/s}^2 \) (acceleration due to gravity)

Substituting the values into the equation:
\[ 49 = 0 \cdot t + \frac{1}{2} \cdot 9.8 \cdot t^2 \]
This simplifies to:
\[ 49 = 4.9 t^2 \]

### Step 3: Solve for time \( t \)
Rearranging the equation gives:
\[ t^2 = \frac{49}{4.9} \]
Calculating this:
\[ t^2 = 10 \quad \Rightarrow \quad t = \sqrt{10} \approx 3.16 \, \text{s} \]

### Step 4: Analyze the horizontal motion
The ball experiences a constant horizontal acceleration due to the wind. This means that while the ball is falling, it is also moving horizontally. The horizontal distance traveled will depend on the horizontal acceleration and the time of flight.

### Step 5: Determine the path of the ball
Since the ball has both vertical and horizontal components of motion, the path followed by the ball will be a curved trajectory (specifically a parabolic path) rather than circular or straight.

### Step 6: Evaluate the options
1. **Path of the ball is circular** - Incorrect, as the path is not circular.
2. **Path of the ball is curved** - Correct, as the ball follows a parabolic trajectory.
3. **Time taken by the ball to reach the ground is 3.16 seconds** - Correct, as calculated.
4. **Actual distance traveled by the ball is less than 49 meters** - Incorrect, as the horizontal motion means the total distance traveled is greater than 49 meters.

### Conclusion
The correct statements are:
- The path of the ball is curved.
- The time taken by the ball to reach the ground is 3.16 seconds.