An aircraft travelled from Calabar to Kano as follows:it flew to Imprint covering a distance of 300km ,30degrees west of North and then flew 400km 60degrees.
do it the same way as the previous one. However angles are left of y axis
(north) component = 300 cos 30 + 400 cos 60
(west) component = 300 sin 30 + 400 sin 60
again sqrt (north^2+west^2)
angle west of north = tan^-1 (west/north)
subtract from 360 to get compass angle, add to 90 to get math text angle
500km
To find the final displacement of the aircraft from Calabar to Kano, we can break down the flight into two separate components: the northward component and the westward component.
1. Northward Component:
The aircraft flew 300 km, 30 degrees west of north. This can be visualized as a right-angled triangle, where the hypotenuse represents the distance flown (300 km) and the opposite side represents the northward component. Using trigonometry, we can find the northward component.
As the angle is given relative to north, we need to find the angle relative to the positive y-axis. Since the angle is west of north, we subtract 90 degrees from it.
Angle relative to positive y-axis = 180 degrees - 90 degrees - 30 degrees = 60 degrees
Using sine function:
northward component = hypotenuse * sin(angle relative to positive y-axis)
northward component = 300 km * sin(60 degrees) = 300 km * 0.866 = 259.8 km (approx.)
2. Westward Component:
The aircraft flew 400 km, 60 degrees. Similar to the northward component, we can use trigonometry to find the westward component.
Using cosine function:
westward component = hypotenuse * cos(angle)
westward component = 400 km * cos(60 degrees) = 400 km * 0.5 = 200 km
Therefore, the northward component is approximately 259.8 km and the westward component is 200 km. Now, we can find the final displacement.
To find the final displacement, we can use the Pythagorean theorem:
displacement^2 = (northward component)^2 + (westward component)^2
displacement^2 = (259.8 km)^2 + (200 km)^2
displacement^2 = 67336.04 km^2 + 40000 km^2
displacement^2 = 107336.04 km^2
displacement = sqrt(107336.04 km^2) ≈ 327.85 km
Therefore, the final displacement of the aircraft from Calabar to Kano is approximately 327.85 km.