Aboat travels at 15 m/s in a direction 45° east of north. the boat then turns and travels at 18 m/s in a direction 5°
north of east.
what is the magnitude of the boat's resultant velocity? round your answer to the nearest whole number.
m/s
what is the direction of the boat's resultant velocity? round your answer to the nearest whole degree.
º 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

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

R ≅ 31.0 m/s

The direction of the resultant velocity is north of east

The direction of the resultant velocity is

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