Solve for the resultant displacement of the two vectors: A = 2.3 km at 45 degrees B = 4.8 km at 90 degrees

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

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