Question

Three vectors , , and , each have a magnitude of 52.0 m and lie in an xy plane. Their directions relative to the positive direction of the x axis are 29.0 ˚, 191 ˚, and 311 ˚, respectively. What are (a) the magnitude and (b) the angle of the vector (relative to the +x direction in the range of (-180°, 180°)), and (c) the magnitude and (d) the angle of in the range of (-180°, 180°)? What are (e) the magnitude and (f) the angle (in the range of (-180°, 180°)) of a fourth vector such that ?

Answer 1

a) A´= A

b) θ₁´ = 29º, θ₂´ = - 169º , θ₃´ = -49º

Step-by-step explanation:

In this exercise you are asked to give the magnitudes and angles of the vectors from another system of

reference

a) The magnitudes

The magnitude of a vector, the size of which is a scalar, this does not depend on the reference system, since it is obtained by subtracting the coordinates of the end point minus the coordinate of the origin of the vector

A =
`x_(f)`- x₀

if the vectors are measured in another reference frame

x_{f}´ = xx_{f}- U

x₀´ = x₀ -U

where U is the distance between the two reference frames

A´ = x_{f}´ - x₀´

we substitute

A´ = (x_{f} - U) - (x₀-U) = x_{f} - x₀

A´ = A

it does not change

b) Angles

The given angles are measured from the positive part of the x axis in a counterclockwise direction, it is asked to give these angles from the x axis

θ₁ = 29º

does not change

θ₁´ = 29º

θ₂ = 191º

we measure clockwise

θ₂´ = θ₂ - 360

θ₂´ = 191 - 360

θ₂´ = - 169º

θ₃ =311º

we measure clockwise

θ₃´ = 311 -360

θ₃´ = -49º