Respuesta :
Answer:
a) R = 3.82 m, b) θ' = 222.9°
Explanation:
We can solve this displacement exercise using vectors, let us write the displacements in a Cartesian coordinate system, where the x-axis is in the East-West direction and the y-axis in the North-South direction
d₁ = 3.1 j ^
d₂ = -2.8 i ^
d₃ = -5.7 j ^
We look for the displacements is each axis
X axis
X = d₂
X = -2.8 i ^
Y Axis
Y = d₁ + d₃
Y = 3.1 - 5.7
Y = - 2.6 j ^
a) For total displacement let's use the Pythagorean theorem
R = √ x² + y²
R = √ 2.8² + 2.6²
R = 3.82 m
b) for the angle we can use trigonometry
tan θ = y / x
θ = tan⁻¹ y / x
θ = tan⁻¹ (-2.6 / -2.8)
θ = 42.9°
The angle respect to x axis is
θ' = 180 + 42.9
θ' = 222.9°
