Respuesta :
Answer:
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:
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, [tex]d_{e}=30 \;\rm cm[/tex]
Distance travelled northward is, [tex]d_{n}= 25 \;\rm cm[/tex].
Distance travelled westward is, [tex]d_{w}=15 \;\rm cm[/tex].
The net displacement covered by ant in eastward direction is,
[tex]d_{net}=d_{e}-d_{w}\\d_{net}=30 \;\rm cm-15 \;\rm cm\\d_{net}=15 \;\rm cm[/tex]
The displacement relative to the original position is,
[tex]d_{resultant}=\sqrt{d^{2}_{net}+d^{2}_{n}} \\d_{resultant}=\sqrt{15^{2}+25^{2}} \\d_{resultant}=29.15 \;\rm cm[/tex]
The angle relative to the original position is,
[tex]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)[/tex]
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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https://brainly.com/question/12874363?referrer=searchResults
