Question

A train is travelling at 40 km/hr in a west direction near a road along which a car moves at 60 kml hr at an angle of 30degree west of north find the direction and the speed of car as it appears to a man in the train.​

Answer 1

Using trigonometry, the north component of the car's velocity is calculated as 60 km/hr * sin(30 degrees), and the west component is determined as 60 km/hr * cos(30 degrees).

Step-by-step explanation:

In order to determine the apparent direction and speed of the car as perceived by a man in the train, the car's velocity is dissected into north and west components.

The car is observed to be moving at 60 km/hr at an angle of 30 degrees west of north.

Employing trigonometry, the north component of the car's velocity is calculated as 60 km/hr * sin(30 degrees), and the west component is determined as 60 km/hr * cos(30 degrees).

As the car seems to be moving in the opposite direction to the train, namely west, the perceived direction is west.

To ascertain the apparent speed of the car, the magnitude of its velocity components is computed using the Pythagorean theorem, expressed as sqrt((north component)^2 + (west component)^2).

This method enables a comprehensive understanding of how the car's motion is perceived from the perspective of an observer in the moving train.