A ship is 50km N.E of Durban harbour and it steams N for 4 hours at 15km/h.
Determine it's position with reference to the harbour.
it started at 35.35 N and 35.35E
4 hr * 15km/hr = 60 km
so its position was 95.35 N and 35.35 E
To determine the ship's position with reference to the harbour, we need to calculate the distance traveled by the ship in the N direction.
The ship steams N for 4 hours at a speed of 15 km/h. Therefore, the distance traveled in the N direction is:
Distance = Speed × Time
Distance = 15 km/h × 4 hours
Distance = 60 km
So, the ship has traveled 60 km in the N direction.
Since the ship was initially 50 km N.E of Durban harbour, we can determine its final position by drawing a right-angled triangle. The 50 km distance to the north-east can be considered as the hypotenuse of the triangle, while the distance traveled in the N direction (60 km) will be the side opposite the right angle.
Using the Pythagorean theorem, we can calculate the remaining side of the triangle, which will represent the distance of the ship from the harbour:
Distance^2 = (N.E distance)^2 + (N distance)^2
Distance^2 = 50 km^2 + 60 km^2
Distance^2 = 2500 km^2 + 3600 km^2
Distance^2 = 6100 km^2
Taking the square root of both sides, we get:
Distance = √6100 km
Distance ≈ 78.14 km
Therefore, the ship's position with reference to the harbour is approximately 78.14 km away in the N direction.
To determine the ship's position with reference to the harbor, we can use the information provided and follow these steps:
1. Start by noting the ship's initial position, which is 50km northeast (N.E) of Durban harbour.
2. The ship steams north (N) for 4 hours at a speed of 15km/h.
3. To find the distance traveled, we can multiply the speed (15km/h) by the time (4 hours), which gives us 60km.
4. Since the ship steams north (N), the distance traveled is directly north from the initial position.
5. Therefore, the final position of the ship, with reference to the harbor, is 60km directly north of Durban harbour.
So, the ship's position is 60km north of Durban harbour.