8. an ant on a picnic table travels 30 cm eastward, then 25 cm northward, and finally 15 cm westward. what is the ant's displacement, angle, and direction
relative to its original position?

The displacement relative to original position is 15 cm.

The angle relative to original position is 30.96 degree.

The direction relative to original position is North-East direction.

Explanation:

Given data:

Distance travelled eastward is,

Distance travelled northward is, .

Distance travelled westward is, .

The net displacement covered by ant in eastward direction is,

The displacement relative to the original position is,

The angle relative to the original position is,

Thus, angle relative to original position is 30.96 degree.

The direction of ant relative to the original position is North-East.

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The displacement of the ant, R = 29.15 cm

The angle of the resultant displacement with its original position is, θ = 30° 57'

The direction of the displacement is towards the northeast.  

Explanation:

Given data,

The displacement towards east, d₁ = 30 cm

The displacement towards north, d₂ = 25 cm

The displacement towards  west, d₃ = 15 cm

The total displacement towards east,

                                       d₄ = d₁ - d₃

                                           = 30 - 15

                                           = 15 cm

The total displacement of ant is given by the resultant displacement,

                            R = √(d₂² + d₄² + 2· d₂ d₄ CosФ)

Where Ф is the angle between the vectors, d₂ & d₄

                                                Ф = 90°

Therefore,

                               R = √(d₂² + d₄²)

Substituting in the above equation,

                               R = √(25² + 15²)

                                  = 29.15 cm

Hence, the displacement of the ant, R = 29.15 cm

The angle of the resultant displacement with its original position is,

                                θ = tan⁻¹ (d₄ / d₂)

                                   = tan⁻¹ (15 / 25)

                                   = tan⁻¹ 0.6

                                   = 30° 57'

Hence, the angle of the resultant displacement the its original position is, θ = 30° 57'

The direction of the displacement is towards the northeast.                                            

molecules are free to separate from each other and will take on the shape of the container. molecules move completely at random and high speeds. they vibrate in a fixed position and do not move around much. molecules expand to the edge of their container.