A thief running away on a straight road on a jeep moving with a speed of 9m/s. A police man chases him on a motor cycle moving at a speed of 10m/s. If the instantaneous separation of jeep from the motor cycle is 100m, how long will it take for the policemen to catch the thief?

Options

A. 1 second
B. 19 second
C. 90 second
D. 100 second

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: Identify the speeds of the thief and the policeman.
- Speed of the thief (on the jeep) = 9 m/s
- Speed of the policeman (on the motorcycle) = 10 m/s

### Step 2: Determine the relative speed of the policeman with respect to the thief.
The relative speed is calculated by subtracting the speed of the thief from the speed of the policeman:
\[ \text{Relative Speed} = \text{Speed of Policeman} - \text{Speed of Thief} \]
\[ \text{Relative Speed} = 10 \, \text{m/s} - 9 \, \text{m/s} = 1 \, \text{m/s} \]

### Step 3: Calculate the initial separation distance.
The initial separation distance between the policeman and the thief is given as:
\[ \text{Initial Separation} = 100 \, \text{m} \]

### Step 4: Use the relative speed to find the time taken to close the separation distance.
To find the time taken for the policeman to catch the thief, we 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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