Answer:
a) the magnitude is 6.37 m/s
b) the direction relative to due west, as seen by Barbara is 46.37° north of west
Explanation:
Given the data in the question;
Barbara is skating due south at a speed of 4.6 m/s
Neil is skating due west at a speed of 4.4 m/s
so
[tex]u_{B}[/tex]→ = 4.6 (-j^)
[tex]u_{N}[/tex]→ = 4.4 (-i^)
[tex]u_{NB}[/tex]→ = [tex]u_{N}[/tex]→ - [tex]u_{B}[/tex]→ = 4.4 (-i^) - 4.6 (-j^)
= -4.4i^ + 4.6j^
a) magnitude
magnitude |([tex]u_{NB}[/tex]→ )| = √( (-4.4)² + (4.6)²)
= √( 19.36 + 21.16)
= √40.52
= 6.37 m/s
Therefore, the magnitude is 6.37 m/s
b) direction relative to due west, as seen by Barbara.
using SOH CAH TOA
tan = opp / adj
so direction will be;
∅ = tan⁻¹( 4.6 / -4.4)
∅ = tan⁻¹( - 1.0454545 )
∅ = - 46.37°
Therefore, the direction relative to due west, as seen by Barbara is 46.37° north of west
