Physics, 06.12.2019 07:31 luisgonz5050

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?

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Answer from: itujggkmjf8067

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, $d_{e}=30 \;\rm cm$

Distance travelled northward is, $d_{n}= 25 \;\rm cm$ .

Distance travelled westward is, $d_{w}=15 \;\rm cm$ .

The net displacement covered by ant in eastward direction is,

$d_{net}=d_{e}-d_{w}\\d_{net}=30 \;\rm cm-15 \;\rm cm\\d_{net}=15 \;\rm cm$

The displacement relative to the original position is,

$d_{resultant}=\sqrt{d^{2}_{net}+d^{2}_{n}} \\d_{resultant}=\sqrt{15^{2}+25^{2}} \\d_{resultant}=29.15 \;\rm cm$

The angle relative to the original position is,

$tan\theta=\dfrac{d_{net}}{d_{n}} \\\theta=tan^{1}(\dfrac{d_{net}}{d_{n}}) \\\theta=tan^{1}(\dfrac{15}{25})\\\theta=30.96 \;\rm degree (North-East)$

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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Answer from: darkpain8913

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.

Answer from: Quest

where's the following? you gotta add it to know what the choices are

explanation:

Answer from: Quest

The speed was not exceeded so it was slow

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8. an ant on a picnic table travels 30 cm eastward, then 25 cm northward, and finally 15 cm westward...

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