A train of `150 m` length is going toward north direction at a speed of `10 ms^-1`. A parrot flies at a speed of `5 ms^-1` toward south direction parallel to the railway track. The time taken by the parrot to cross the train is equal to.

Options

A. `12s`
B. `8s`
C. `15s`
D. `10s`

Answer

To solve the problem, we need to find the time taken by the parrot to cross the train. Here’s a step-by-step breakdown of the solution:

### Step 1: Identify the given data
- Length of the train (L) = 150 m
- Speed of the train (V_train) = 10 m/s (toward the north)
- Speed of the parrot (V_parrot) = 5 m/s (toward the south)

### Step 2: Determine the relative velocity
Since the train and the parrot are moving in opposite directions, we can find the relative velocity (V_relative) by adding their speeds:
\[ V_{\text{relative}} = V_{\text{train}} + V_{\text{parrot}} = 10 \, \text{m/s} + 5 \, \text{m/s} = 15 \, \text{m/s} \]

### Step 3: Calculate the time taken to cross the train
The time (t) taken by the parrot to cross the train can be calculated using the formula:
\[ t = \frac{\text{Distance}}{\text{Relative Velocity}} \]
Here, the distance is the length of the train (150 m), and the relative velocity is 15 m/s:
\[ t = \frac{150 \, \text{m}}{15 \, \text{m/s}} = 10 \, \text{s} \]

### Final Answer
The time taken by the parrot to cross the train is **10 seconds**.

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