what is the direction of the acceleration of the sailboat, expressed as an angle in degrees of north of east

Magnitude of acceleration, a = 1.90 m/s²

Direction of the acceleration, α = N24.9°E

Note: The question is incomplete. The complete question is given below:

A sailboat has a mass of 2160 kg and experiences two horizontal forces. One is due to the action of the water on the hull of the boat and is directed east and has a magnitude of 1990 N. The other is due to the action of the wind on the sails and is directed northeast with a magnitude of 2440 N.

What is the magnitude of the acceleration of the sailboat in m/s2?

What is the direction of the acceleration of the sailboat, expressed as an angle in degrees north of east?

Explanation:

The the vector sum of all the forces constitute the net force acting on the sailboat.

Resolving the forces into horizontal and vertical components:

Horizontal forces:

X = 1990 cos90 +  

2440 cos 45°

X = 1725 N

Vertical forces:

Y = 1990 sin90° + 2440 sin45°

Y = (1990 + 1725) N

Y = 3715 N

Net force,  F = √(X² + Y²)

F = √(1725² + 3715²)

F = 4095.5 N

According to Newton's law, Net force causes acceleration, a, of a body

Net force = mass * acceleration  

a = (Net force)/m

a = 4095.5/2160

a = 1.90 m/s²

Magnitude of acceleration, a = 1.90 m/s²

Direction of the acceleration, α = tan⁻¹ (Y/X)

α = tan⁻¹ (3715/1725)

α = 65.1

Direction of the acceleration, α, North of east = 90 - 65.1°

Direction of the acceleration, α = N24.9°E

d) physical means can be used to separate the components of air.

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