Respuesta :

Answer:

The displacement from starting point, x = 2.236 km.

Direction of the displacement = 26.56 degrees with repect to east measured anticlockwise.

Explanation:

Given that a driver drives 1 km north and 2 km east.

such that from the strating point, he travels towards north and then east such that the angle between them is 90 degrees.

Visualise the situation to a right anged triangle

and the line joining the starting point and the ending point will be the hypotenuse of the traingle.

By pythogoras theorm,

[tex]x^{2} = a^{2} + b^{2}[/tex]

where a = 1 km and b = 2 km

[tex]x^{2} = 1^{2} + 2^{2}[/tex]

[tex]x^{2} = 5\\x = \sqrt{5}[/tex]

The displacement from starting point, x = 2.236 km

The distance travelled by the driver = 2.236 km.

Direction of the displacement = atan ([tex]\frac{1}{2}[/tex])

  =  26.56 degrees with repect to east measured anticlockwise.

The driver's distance is 2.24 km in the North-east direction from the starting point.

An illustrative diagram is attached below

In the diagram, S indicates the starting point and F is the final position.

The driver's distance from the starting point can be determined by calculating the length of /SF/

By Pythagoras' theorem,

[tex]/SF/^{2} = /PS/^{2} +/FP/^{2}[/tex]

From the given information

/PS/ = 1 km

and /FP/ = 2 km

Then,

[tex]/SF/^{2} = 1^{2} + 2^{2}[/tex]

[tex]/SF/^{2} = 1 + 4[/tex]

[tex]/SF/^{2} = 5[/tex]

[tex]/SF/ = \sqrt{5} \ km[/tex]

/SF/ = 2.24 km

Hence. the driver's distance from the starting point is 2.24 km.

As shown in the diagram, she is in the North-east direction from the starting point.

Learn more on calculating distance here: https://brainly.com/question/16394460

Ver imagen Abdulazeez10