An aircraft travelled from calabar to kano as follows; it flew first to ilorin covering a distance of 300km, 30degree West or North , and then flew 400km, 60degree east of north to kano. what is the resultant displacement?
30° west of north = 120°
60° east of north = 30°
using vectors:
R = (300cos120, 300sin120) + (400cos30, 400 sin30)
= (-150, 150√3) + (200√3 , 200) = (200√3-150,150√3+200)
= (196.41, 459.81)
maginitude = √(196.41^2 + 459.81^2) = 500
angle = tan^-1(459.81/196.41) = appr 66.87°
or
make a sketch and use the cosine law:
R^2 = 300^2 + 400^2 - 2(300)(400)cos90°
= 500
leaving it up to you to find the angle using the sine law in the triangle, it should be the same as my first solution.
Pls show a diagrammatical representation
Must the two degrees be added together??
An aircraft travelled from calabar to kano as follows; it flew first to ilorin covering a distance of 300km, 300 West or North , and then flew 400km, 600 east of north to kano. what is the resultant displacement?
It's very easy to understand.
To find the resultant displacement of the aircraft, we need to combine the two given displacements - the one from Calabar to Ilorin and the one from Ilorin to Kano.
Let's start by drawing a diagram to visualize the situation:
```
C (Calabar)
↓
↑ 300km, 30° W or N
I (Ilorin)
↑
↑ 400km, 60° E of N
K (Kano)
```
Now, let's break down the displacements into their horizontal (x-axis) and vertical (y-axis) components using trigonometry.
For the displacement from Calabar to Ilorin:
- Horizontal component (x): 300 km * sin(30°) = 150 km
- Vertical component (y): 300 km * cos(30°) = 259.81 km (rounded to the nearest hundredth)
For the displacement from Ilorin to Kano:
- Horizontal component (x): 400 km * sin(60°) = 346.41 km (rounded to the nearest hundredth)
- Vertical component (y): 400 km * cos(60°) = 200 km
Now, let's add up the horizontal and vertical components separately to find the resultant displacement:
Horizontal component: 150 km + 346.41 km = 496.41 km (rounded to the nearest hundredth)
Vertical component: 259.81 km + 200 km = 459.81 km (rounded to the nearest hundredth)
Finally, we can use the Pythagorean theorem to find the magnitude of the resultant displacement:
Resultant displacement = √((horizontal component)^2 + (vertical component)^2)
= √((496.41 km)^2 + (459.81 km)^2)
= √(246425.08 km^2 + 211206.98 km^2)
= √457632.06 km^2
= 676.77 km (rounded to the nearest hundredth)
Therefore, the resultant displacement of the aircraft from Calabar to Kano is approximately 676.77 km.