An arrow is projected into air. It's time of flight is 5seconds and range 200m. , the vertical component of the velocity is:-

Options

A. `25m//s`
B. `40m//s`
C. `12.5m//s`
D. `31.25m//s`

Explanation

To find the vertical component of the velocity of the arrow projected into the air, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**:
We are given the time of flight (T) as 5 seconds and the range (R) as 200 meters. We need to find the vertical component of the initial velocity (Vy).

2. **Use the Time of Flight Formula**:
The time of flight for a projectile is given by the formula:
\[ T = \frac{2Vy}{g} \]
where \( g \) is the acceleration due to gravity (approximately \( 10 \, \text{m/s}^2 \)).

3. **Rearrange the Formula**:
We can rearrange the formula to solve for \( Vy \):
\[ Vy = \frac{gT}{2} \]

4. **Substitute the Known Values**:
Substitute \( T = 5 \, \text{s} \) and \( g = 10 \, \text{m/s}^2 \) into the equation:
\[ Vy = \frac{10 \times 5}{2} \]

5. **Calculate**:
\[ Vy = \frac{50}{2} = 25 \, \text{m/s} \]

6. **Conclusion**:
The vertical component of the velocity is \( 25 \, \text{m/s} \).

### Final Answer:
The vertical component of the velocity is \( 25 \, \text{m/s} \).

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