If two projectile of same mass are thrown at an angle of 50° and 40° with the horizontal with the same speed then, which of the following statement is true?

Options

A. Time of flight of both projectile is same
B. Maximum height acquired by both projectiles is same
C. Horizontal range of both projectiles is Same
D. None of these

Answer

To solve the problem, we need to analyze the projectile motion of two objects thrown at different angles but with the same initial speed. We will evaluate the time of flight, maximum height, and horizontal range for both projectiles.

### Step-by-Step Solution:

1. **Understanding the Problem**:
We have two projectiles thrown at angles of 50° and 40° with the same initial speed (u). We need to determine which statement regarding their motion is true.

2. **Time of Flight**:
The formula for the time of flight (T) of a projectile is given by:
\[ T = \frac{2u \sin \theta}{g} \]
where \( g \) is the acceleration due to gravity. Since the angles (50° and 40°) are different, the sine values will also be different. Thus, the time of flight for both projectiles will not be the same.

**Conclusion**: The time of flight for both projectiles is not the same.

3. **Maximum Height**:
The formula for the maximum height (H) reached by a projectile is:
\[ H = \frac{u^2 \sin^2 \theta}{2g} \]
Similar to the time of flight, since the angles are different, the sine values will differ. Therefore, the maximum heights for both projectiles will also be different.

**Conclusion**: The maximum height acquired by both projectiles is not the same.

4. **Horizontal Range**:
The formula for the horizontal range (R) of a projectile is:
\[ R = \frac{u^2 \sin 2\theta}{g} \]
Here, we need to evaluate \( \sin 2\theta \) for both angles:
- For \( \theta_1 = 50° \):
\[ \sin 2\theta_1 = \sin 100° \]
- For \( \theta_2 = 40° \):
\[ \sin 2\theta_2 = \sin 80° \]

We know that:
\[ \sin 100° = \sin(90° + 10°) = \cos 10° \quad \text{and} \quad \sin 80° = \sin(90° - 10°) = \cos 10° \]
Therefore, \( \sin 100° = \sin 80° \). This means:
\[ R_1 = R_2 \]
Hence, the horizontal range for both projectiles is the same.

**Conclusion**: The horizontal range for both projectiles is the same.

### Final Answer:
The correct statement is that the horizontal range for both projectiles is the same.

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