Relative Velocity of the Helicopter as Seen by the Passengers in the Train

When considering the relative velocity of the helicopter as seen by the passengers in the train, we need to take into account both the speed and direction of each object. In this scenario, the helicopter is moving south with a speed of 50 km/h, while the train is moving towards the east with the same speed.

Understanding Relative Velocity

Relative velocity refers to the velocity of an object with respect to another object. It is the vector difference between the velocities of the two objects. When calculating relative velocities, we must consider the velocities of both objects and their directions.

Vector Addition of Velocities

To determine the relative velocity of the helicopter as seen by the passengers in the train, we need to add the velocities of the helicopter and the train vectorially.

Velocity of the Helicopter
- Magnitude: 50 km/h
- Direction: South

Velocity of the Train
- Magnitude: 50 km/h
- Direction: East

Vector Addition

To add the velocities vectorially, we can use the parallelogram method or the head-to-tail method.

Parallelogram Method:
1. Draw the vectors representing the velocities of the helicopter and the train as adjacent sides of a parallelogram.
2. Complete the parallelogram by drawing the diagonal.
3. The diagonal represents the resultant vector, which is the relative velocity of the helicopter as seen by the passengers in the train.

Head-to-Tail Method:
1. Draw the vector representing the velocity of the helicopter.
2. Place the vector representing the velocity of the train head-to-tail with the helicopter's vector.
3. The resultant vector, drawn from the tail of the helicopter's vector to the head of the train's vector, represents the relative velocity of the helicopter as seen by the passengers in the train.

Resultant Vector

Using either method, we can determine that the resultant vector points in a direction between south and east. Therefore, the relative velocity of the helicopter as seen by the passengers in the train will be towards the southeast.

Conclusion

The relative velocity of the helicopter as seen by the passengers in the train will be towards the southeast. This means that from the perspective of the train passengers, the helicopter appears to be moving in a direction between south and east.

South west