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 a straight line
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 more then 49 m.

Explanation

To solve the problem step by step, we will analyze the motion of the ball dropped from a height of 49 m under the influence of gravity and horizontal acceleration due to wind.

### Step 1: Understanding the Motion
The ball is dropped from a height of 49 m, which means it has an initial vertical velocity (u) of 0 m/s. The only force acting on it in the vertical direction is gravity, which accelerates it downwards at approximately 9.81 m/s² (we can approximate this as 10 m/s² for simplicity).

### Step 2: Analyzing Horizontal Motion
The wind provides a constant horizontal acceleration (let's denote it as \( a \)). Since the ball is dropped, it starts with an initial horizontal velocity of 0 m/s. The horizontal motion is independent of the vertical motion.

### Step 3: Path of the Ball
The ball will follow a parabolic trajectory due to the combination of vertical motion (under gravity) and horizontal motion (due to wind). Therefore, the path of the ball will not be a straight line; it will be a curved path.

### Step 4: Time to Reach the Ground
To find the time taken for the ball to reach the ground, we can use the second equation of motion for the vertical direction:
\[ s = ut + \frac{1}{2} a t^2 \]
Where:
- \( s = 49 \) m (the height from which the ball is dropped)
- \( u = 0 \) m/s (initial vertical velocity)
- \( a = g = 10 \) m/s² (acceleration due to gravity)

Substituting the values:
\[ 49 = 0 + \frac{1}{2} \times 10 \times t^2 \]
\[ 49 = 5t^2 \]
\[ t^2 = \frac{49}{5} = 9.8 \]
\[ t = \sqrt{9.8} \approx 3.16 \text{ seconds} \]

### Step 5: Distance Travelled
The actual distance travelled by the ball will be more than 49 m because it follows a curved path. The vertical distance is the height dropped (49 m), but the horizontal motion due to wind means the ball travels along a longer path (the hypotenuse of the triangle formed by the vertical and horizontal distances).

### Conclusion
Based on the analysis:
- **Statement A**: The path of the ball is a straight line. (Incorrect)
- **Statement B**: The path of the ball is a curved line. (Correct)
- **Statement C**: The time taken by the ball to reach the ground is approximately 3.16 seconds. (Correct)
- **Statement D**: The actual distance travelled by the ball is more than 49 meters. (Correct)

### Correct Statements
Therefore, the correct statements are B, C, and D.