The time of fight of an object projected with speed ` 20 ms^(-1)` at an angle ` 30^(@)` with the horizontal , is

Options

A. 1 s
B. 4 s
C. 2 s
D. 6s

Answer

To solve the problem of finding the time of flight of an object projected with a speed of \( 20 \, \text{m/s} \) at an angle of \( 30^\circ \) with the horizontal, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values:**
- Initial speed \( u = 20 \, \text{m/s} \)
- Angle of projection \( \theta = 30^\circ \)
- Acceleration due to gravity \( g = 10 \, \text{m/s}^2 \) (approximately)

2. **Use the formula for time of flight:**
The formula for the time of flight \( t \) of a projectile is given by:
\[ t = \frac{2u \sin \theta}{g} \]

3. **Calculate \( \sin \theta \):**
For \( \theta = 30^\circ \):
\[ \sin 30^\circ = \frac{1}{2} \]

4. **Substitute the values into the formula:**
Now substitute \( u = 20 \, \text{m/s} \), \( \sin 30^\circ = \frac{1}{2} \), and \( g = 10 \, \text{m/s}^2 \) into the time of flight formula:
\[ t = \frac{2 \times 20 \times \frac{1}{2}}{10} \]

5. **Simplify the equation:**
\[ t = \frac{2 \times 20 \times 0.5}{10} = \frac{20}{10} = 2 \, \text{s} \]

6. **Conclusion:**
The time of flight of the object is \( 2 \, \text{seconds} \).

### Final Answer:
The time of flight of the object is \( 2 \, \text{seconds} \).

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