Respuesta :
Answer:
R = 10.06 m, θ = 28.7º
Explanation:
o find the total displacement the best way is to find the displacement in the x (East) and y (North) axes
let's decompose the displacements
d₂ = 4 m
θ₂ = 45
let's use trigonometry
cos 45 = x₂ / d₂
sin 45 = y₂ / d₂
x₂ = d₂ cos 45
y₂ = d₂ sin 45
x₂ = 4 cos 45 = 2,828 m
y₂ = 4 sin 45 = 2,828 m
The shredding the x axis is
x_total = x₁ + x₂
x_total = 6 + 2,828
x_total = 8,828 m
The displacement in the y-axis
y_total = y₂ + y₃
y_total = 2,828 + 2
y_total = 4.828 m
Let's use Pythagoras' theorem for total displacement
R = [tex]\sqrt{x_{total}^2 + y_{total}^2 }[/tex]
R = [tex]\sqrt{8.828^2 + 4.828^2 }[/tex]
R = 10.06 m
for the direction let's use trigonometry
tan θ = [tex]\frac{x_{total} }{y_{total} }[/tex]
θ = tan⁻¹ \frac{x_{total} }{y_{total} }
θ = tan⁻¹ [tex]\frac{ 4.828}{ 8.828}[/tex]
θ = 28.7º
this angle is measured counterclockwise from the positive side of the x axis (Eat)
