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.
