A railway engine starts shunting wagons by first going 1000 m north of railway station. It reverses and travels 1250 m south and then it again moves 600 m north. Finally moving 800 m south it comes to rest. How far is the engine from the station and in which direction?
1000 - 1250 + 600 - 800 = -450 = 450 m south of the station
And
To find the direction and distance of the engine from the station, we can use the concept of displacement.
Let's break down the given information step by step:
1. The engine starts by moving north of the railway station for 1000 m.
This means the engine's displacement is +1000 m (north).
2. The engine then reverses and moves 1250 m south.
Adding this to the previous displacement, the total displacement becomes +1000 m (north) - 1250 m (south) = -250 m (south).
3. Next, the engine moves back in the north direction for 600 m.
Adding this to the previous displacement, the total displacement becomes -250 m (south) + 600 m (north) = +350 m (north).
4. Lastly, the engine moves 800 m south and comes to rest.
Adding this to the previous displacement, the total displacement becomes +350 m (north) - 800 m (south) = -450 m (south).
Therefore, the engine is located 450 m south of the railway station.
To determine the distance and direction of the engine from the station, we can visualize the movements on a graph.
Let's consider the railway station as a reference point (0,0) on the graph. The initial movement of the engine takes it 1000m north, so its new position is (0,1000).
Next, it reverses and travels 1250m south, which means it moves down on the graph by 1250 units. The new position becomes (0,1000-1250) or (0,-250).
Then, the engine moves 600m north from its current position, leading to a new position of (0,-250+600) or (0,350).
Finally, it moves 800m south, resulting in a new position of (0,350-800) or (0,-450).
From the final position (0,-450) on the graph, we can calculate the distance from the station using the Pythagorean theorem:
Distance = √(0^2 + (-450)^2)
= √(0 + 202,500)
= √202,500
= 450 units (approximately)
Therefore, the engine is approximately 450 meters away from the station. Since it is to the south of the station, the direction is south.