A ship sets sail from Rotterdam, The Netherlands, heading due north at 8.00 m/s relative to the water. The local ocean current is 1.52 m/s in a direction 40° north of east. What is the velocity of the ship relative to the earth?.

Respuesta :

Answer:

The velocity of the ship relative to the earth V = 9.05 [tex]\frac{m}{s}[/tex]

Explanation:

The local ocean current is  = 1.52 m/s

Direction [tex]\theta[/tex] = 40°

Velocity component in X - direction [tex]V_{x}[/tex] = 1.52 [tex]\cos 40[/tex]°

[tex]V_{x}[/tex] = 1.164 [tex]\frac{m}{s}[/tex]

Velocity component in Y - direction [tex]V_{y}[/tex] = 8 + 1.52 [tex]\sin 40[/tex]°

[tex]V_{y}[/tex] = 8.97 [tex]\frac{m}{s}[/tex]

The velocity of the ship relative to the earth

[tex]V = \sqrt{V_{x}^{2} + V_{y} ^{2} }[/tex]

Put the values of [tex]V_{x}[/tex] and [tex]V_{y}[/tex] we get,

⇒ [tex]V = \sqrt{1.164^{2} + 8.97 ^{2} }[/tex]

⇒ V = 9.05 [tex]\frac{m}{s}[/tex]

This is the velocity of the ship relative to the earth.

Answer:

Second part of question on cengage: Earth in degrees north of east?=  82.61

Explanation:

tan-1= (8.97/1.164)

82.61