An air craft travelled from calabar to kano as follows, it flew first to illori covering a distance of 300km, 30° west of North, and then flew 400km, 60° east of North to kano. What is the resultant displacement? It's urgent
All angles are measured CCW from +x-axis.
Disp. = 300km[120o] + 400km[30o].
Disp. = (300*Cos120+300*sin120)+(400*Cos30+400*sin30),
Disp. = (-150+260i) + (346.4+200i).
Combine like-terms and convert to polar form.
thanks for the answer
Disp. = 196 + 460i = 500km[66.9o].
😂😂😂😂🤣🤣🤣🤣😅😅😅😅🥵😅🤣😂😅🤣😂😅🤣😂😅🤣😂🥵😅🤣😂😅🤣😂😅🤣😂😅__ I DON'T KNOW
To find the resultant displacement, we need to break down the two legs of the aircraft's journey into their respective north and east components.
First, let's find the north and east components for the first leg of the journey, from Calabar to Illorin.
Distance traveled: 300 km
Angle: 30° west of north
To find the north component, we use the sine function:
North component = Distance * sin(Angle)
North component = 300 km * sin(30°)
North component = 150 km
To find the east component, we use the cosine function:
East component = Distance * cos(Angle)
East component = 300 km * cos(30°)
East component = 259.81 km (rounded to two decimal places)
Now, let's find the north and east components for the second leg of the journey, from Illorin to Kano.
Distance traveled: 400 km
Angle: 60° east of north
North component = Distance * sin(Angle)
North component = 400 km * sin(60°)
North component = 346.41 km (rounded to two decimal places)
East component = Distance * cos(Angle)
East component = 400 km * cos(60°)
East component = 200 km
To find the resultant displacement, we add the north and east components together.
Resultant north component = 150 km + 346.41 km
Resultant north component = 496.41 km
Resultant east component = 259.81 km + 200 km
Resultant east component = 459.81 km
Using the Pythagorean theorem, we can find the magnitude of the resultant displacement:
Resultant displacement = √(Resultant north component^2 + Resultant east component^2)
Resultant displacement = √(496.41 km^2 + 459.81 km^2)
Resultant displacement ≈ 678.20 km (rounded to two decimal places)
Therefore, the resultant displacement of the aircraft's journey from Calabar to Kano is approximately 678.20 km.
distance north = N = 300 cos30+400 cos 60
distance east = E = -300 sin 30+400 sin 60
magnitude of displacement = sqrt(N^2+E^2)
angle east of north =tan^-1(E/N)