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 of determining which statement is true regarding two projectiles thrown at angles of 50° and 40° with the same speed, we can analyze the projectile motion equations step by step.

### Step 1: Understanding Time of Flight
The time of flight (T) for a projectile is given by the formula:
\[ T = \frac{2u \sin \theta}{g} \]
where:
- \( u \) is the initial speed,
- \( \theta \) is the angle of projection,
- \( g \) is the acceleration due to gravity.

For the two angles:
- Time of flight for 50°:
\[ T_{50} = \frac{2u \sin 50°}{g} \]
- Time of flight for 40°:
\[ T_{40} = \frac{2u \sin 40°}{g} \]

Since \( \sin 50° \) is not equal to \( \sin 40° \), we can conclude:
\[ T_{50} \neq T_{40} \]
Thus, the first statement is false.

### Step 2: Analyzing Maximum Height
The maximum height (H) of a projectile is given by the formula:
\[ H = \frac{u^2 \sin^2 \theta}{2g} \]

For the two angles:
- Maximum height for 50°:
\[ H_{50} = \frac{u^2 \sin^2 50°}{2g} \]
- Maximum height for 40°:
\[ H_{40} = \frac{u^2 \sin^2 40°}{2g} \]

Since \( \sin^2 50° \) is not equal to \( \sin^2 40° \), we conclude:
\[ H_{50} \neq H_{40} \]
Thus, the second statement is also false.

### Step 3: Evaluating Horizontal Range
The horizontal range (R) of a projectile is given by the formula:
\[ R = \frac{u^2 \sin 2\theta}{g} \]

For the two angles:
- Range for 50°:
\[ R_{50} = \frac{u^2 \sin 100°}{g} \]
- Range for 40°:
\[ R_{40} = \frac{u^2 \sin 80°}{g} \]

Using the identity \( \sin(90° - \theta) = \cos(\theta) \), we can see that:
- \( \sin 100° = \sin(90° + 10°) = \cos 10° \)
- \( \sin 80° = \sin(90° - 10°) = \cos 10° \)

Since \( \sin 100° = \sin 80° \), we find:
\[ R_{50} = R_{40} \]
Thus, the third statement is true.

### Conclusion
The correct statement is that the horizontal range of both projectiles is the same.