A thief is running away on a straitht road in a moving with a speed of `9 ms^(-1)`. A policeman chases him on a motor cycle moving at a speed of `10 ms^(-1)`. If the instananeous separation of the jeep from the motor cycle is `100 m`, how long will it take for the policeman to catch the thief ?.

Options

A. a. `1s`
B. b. `19 s`
C. c. ` 90 s`
D. d. ` 100s`

Explanation

To solve the problem of how long it will take for the policeman to catch the thief, we can follow these steps:

### Step 1: Understand the given information
- Speed of the thief (V_thief) = 9 m/s
- Speed of the policeman (V_police) = 10 m/s
- Initial separation between the thief and the policeman = 100 m

### Step 2: Determine the relative speed
Since both the thief and the policeman are moving in the same direction, we can find the relative speed by subtracting the speed of the thief from the speed of the policeman.

\[ \text{Relative Speed} = V_{\text{police}} - V_{\text{thief}} = 10 \, \text{m/s} - 9 \, \text{m/s} = 1 \, \text{m/s} \]

### Step 3: Calculate the time to catch the thief
To find the time it takes for the policeman to catch the thief, we can use the formula:

\[ \text{Time} = \frac{\text{Distance}}{\text{Relative Speed}} \]

Substituting the values we have:

\[ \text{Time} = \frac{100 \, \text{m}}{1 \, \text{m/s}} = 100 \, \text{s} \]

### Conclusion
The time it will take for the policeman to catch the thief is **100 seconds**.

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