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?
1250-1000 = 250 m south
600-250 = 350 m north
800-350 = 450 m south
So it is 450 m south of station
To find the total distance and direction of the engine from the station, we can break down the movements step-by-step.
1. The engine starts by going 1000 m North of the railway station. This means it is 1000 m away from the station in the North direction.
2. It then reverses and travels 1250 m South. This cancels out the previous North movement and brings the engine 1250 m away from the station in the South direction.
3. Next, it moves 600 m North. This partially cancels out the previous South movement. So, the engine is now 650 m away from the station in the South direction (1250 m - 600 m = 650 m).
4. Finally, it moves 800 m South. This cancels out the remaining North movement and brings the engine 150 m away from the station in the South direction (650 m - 800 m = -150 m).
Therefore, the engine is 150 m away from the station in the South direction.
To find the distance and direction of the engine from the station, we can visualize the movements of the engine on a coordinate plane.
Let's assume the railway station is located at the origin (0,0) on the coordinate plane. The initial movement of the engine is 1000 m North, so it moves up along the positive y-axis to the point (0,1000).
Next, the engine reverses and travels 1250 m South. This means it moves down along the negative y-axis from the point (0,1000) to the point (0,1000-1250) = (0,-250).
Then, the engine moves 600 m North, so it moves up along the positive y-axis from (0,-250) to (0,-250+600) = (0,350).
Finally, the engine moves 800 m South, so it moves down along the negative y-axis from (0,350) to (0,350-800) = (0,-450).
Therefore, the engine is located at the point (0,-450), which means it is 450 m South of the railway station (since the y-coordinate is negative direction), and it is in the South direction from the station.
Thus, the engine is 450 meters South of the station.