Question

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?

Answer 1

Answer:

Magnitude of the acceleration = 1.90 m/s²

Direction of the acceleration = 65.1° (measured counter clockwisely from the +x axis) or 65.1° north of East

Explanation:

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

One force 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; in vector form, F₁ = (1990j) N

The other force is due to the action of the wind on the sails and is directed northeast with a magnitude of 2440 N; in vector form, F₂ = 2440 [(cos 45°)î + (sin 45°)j] N = 1725î + 1725j) N

Net force = F₁ + F₂ = 1990j + (1725î + 1725j) = (1725î + 3715j) N

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

Net force = ma

a = (Net force)/m

a = (1725î + 3715j)/2160 = (0.80î + 1.72j) m/s²

Magnitude of acceleration

/a/ = √[(0.8²) + (1.72²)] = 1.90 m/s²

Direction of the acceleration = tan⁻¹ (1.72/0.8) = 65.1°