Answer:
The resultant of the vector is 6.63 km
Explanation:
Given;
vector A = 2.3 km 45°
vector B = 4.8 km 90°
The vectors in the x - direction is given by;
Aₓ = 2.3 km Cos 45° = 1.6263 km
Bₓ = 4.8 km Cos 90° = 0
The sum of the vectors in x -direction is given by;
∑X = 1.6263 km + 0 = 1.6263 km
The vectors in the y - direction is given by;
Ay = 2.3 km Sin 45 = 1.6263 km
By = 4.8 km Sin 90° = 4.8 km
The sum of the vectors in y -direction is given by;
∑Y = 1.6263 km + 4.8 km = 6.4263 km
The resultant vector is given by;
R = √(X² + Y²)
R = √[(1.6263)² + (6.4263)²]
R = 6.63 km
Therefore, the resultant of the vector is 6.63 km
The resultant displacement of the two vectors A and B is 6.63 Km and this can be determined by using the given data.
Given :
The two vectors: A = 2.3 km at 45 degrees B = 4.8 km at 90 degrees.
In order to determine the resultant displacement, first, determine the vector in x-direction:
[tex]\rm A_x=2.3cos45=1.6263 \;Km[/tex]
[tex]\rm B_x=4.8cos90=0 \;Km[/tex]
Now, the sum of the vectors is given by:
[tex]\rm \sum X=1.6263+0=1.6263\;Km[/tex]
In order to determine the resultant displacement, first, determine the vector in y-direction:
[tex]\rm A_y=2.3sin45=1.6263 \;Km[/tex]
[tex]\rm B_y=4.8sin90=4.8 \;Km[/tex]
Now, the sum of the vectors is given by:
[tex]\rm \sum Y = 1.6263+4.8=6.4263[/tex]
Now, the resultant vector is given by:
[tex]\rm R = \sqrt{X^2+Y^2}[/tex]
[tex]\rm R=\sqrt{(1.6263)^2+(6.4263)^2}[/tex]
R = 6.63 Km
The resultant displacement of the two vectors A and B is 6.63 Km.
For more information, refer to the link given below:
https://brainly.com/question/16380983
