Distance between a frog and an insect on a horizontal plane is 10m. Frog can jump with a maximum speed of `sqrt(10) m//s`. Minimum number of jumps required by the frog to catch the insect is : `g=10 m//s^2`.

Options

A. 5
B. 10
C. 100
D. 50

Explanation

To solve the problem of how many jumps a frog needs to catch an insect located 10 meters away, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Given Values**:
- Distance between the frog and the insect, \( d = 10 \, \text{m} \)
- Maximum speed of the frog, \( u_{\text{max}} = \sqrt{10} \, \text{m/s} \)
- Acceleration due to gravity, \( g = 10 \, \text{m/s}^2 \)

2. **Calculate the Range of One Jump**:
The range \( R \) of a projectile is given by the formula:
\[ R = \frac{u^2 \sin(2\theta)}{g} \]
For maximum range, the angle \( \theta \) should be \( 45^\circ \), where \( \sin(90^\circ) = 1 \). Thus, the formula simplifies to:
\[ R_{\text{max}} = \frac{u^2}{g} \]
Substituting the values:
\[ R_{\text{max}} = \frac{(\sqrt{10})^2}{10} = \frac{10}{10} = 1 \, \text{m} \]

3. **Determine the Number of Jumps Required**:
To find the minimum number of jumps \( n \) required to cover the distance \( d \):
\[ n \cdot R_{\text{max}} = d \]
Substituting the known values:
\[ n \cdot 1 = 10 \]
Therefore:
\[ n = \frac{10}{1} = 10 \]

4. **Conclusion**:
The minimum number of jumps required by the frog to catch the insect is \( n = 10 \).

### Final Answer:
The minimum number of jumps required by the frog to catch the insect is **10 jumps**.

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