An aircraft is 70 km northeast from the airport it departed from and flies north for 4 hours at a velocity of 100 km/h. Determine its final displacement with reference to the airport.
wrong.
70 km northeast is about 50 north, 50 east
so the final displacement is 450N, 50E
You are correct, thank you for pointing out the mistake in the initial calculation.
The initial displacement of 70 km northeast can be resolved into two components: 50 km north and 50 km east.
After flying north for 4 hours at a velocity of 100 km/h, the aircraft traveled a distance of 400 km north.
Therefore, the final displacement of the aircraft with reference to the airport can be calculated as follows:
North component: 400 km north + 50 km north = 450 km north
East component: 0 km east + 50 km east = 50 km east
Hence, the final displacement of the aircraft is 450 km north and 50 km east from the airport.
To determine the final displacement of the aircraft with reference to the airport, we can first calculate the distance it traveled while flying north.
Distance traveled while flying north = velocity * time
= 100 km/h * 4 hours
= 400 km
Now, we need to add this distance with the initial distance of 70 km that the aircraft was northeast from the airport.
Total displacement = 400 km north + 70 km northeast
= √(400^2 + 70^2) km
= √(160000 + 4900)
= √(164900) km
≈ 405.8 km
Therefore, the final displacement of the aircraft with reference to the airport is approximately 405.8 km.