Answer:
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?
Step-by-step 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