Answer:
The magnitude of the boat's resultant velocity is 31.0 m/s
The direction of the boat's resultant velocity is 23.0° north of east
Explanation:
A boat travels at 15 m/s in a direction 45° east of north
The vector of velocity is 15 m/s in direction 45° with north
The horizontal component = 15(m/s) sin(45)° = 10.61 m/s
The vertical component = 15(m/s) cos(45)° = 10.61 m/s
The boat then turns and travels at 18 m/s in a direction 5° north of east
The vector of velocity is 18 m/s in direction 5° with east
The horizontal component = 18(m/s) cos(5)° = 17.93 m/s
The vertical component = 18(m/s) sin(5)° = 1.57 m/s
The horizontal component of the resultant velocity x is
x = 10.61 + 17.93 = 28.54 m/s
The vertical component of the resultant velocity y is
y = 10.61 + 1.57 = 12.18 m/s
The magnitude of the resultant velocity [tex]R=\sqrt{x^{2}+y^{2}}[/tex]
[tex]R=\sqrt{(28.54)^{2}+(12.18)^{2}}=31.03[/tex]
R ≅ 31.0 m/s
The direction of the resultant velocity is [tex]tan^{-1}\frac{x}{y}[/tex] north of east
The direction of the resultant velocity is [tex]tan^{-1}\frac{12.18}{28.54}=23.1[/tex]
α = 23.0° north of east
The magnitude of the boat's resultant velocity is 31.0 m/s
The direction of the boat's resultant velocity is 23.0° north of east
