Answer:
The magnitude of the resultant acceleration is 2.2 [tex]m/s^2[/tex]
Explanation:
Mass (m) of the sailboat = 2000 kg
Force acting on the sailboat due to ocean tide is [tex]F_1[/tex] = 3000N
Eastwards means takes place along the positive x direction
Then[tex]F_{1x}[/tex] = 3000N and [tex]F_{1y}[/tex]= 0
Wind Force acting on the Sailboat is[tex]F_2[/tex] = 6000N directed towards the northwest that means at an angle 45 degree above the negative x axis
Then
[tex]F_{2x}[/tex] = -(6000N) cos 45 degree = -4242.6 N
[tex]F_{2y}[/tex] = (6000N) cos 45 degree = 4242.6 N
Hence , the net force acting on the sailboat in x direction is
[tex]F_x = F_{1x}+ F_{2x}[/tex]
= - 3000 N + 4242.6 N
= - 3000 N +4242.6 N
= 1242.6N
Net Force acting on the sailboat in y direction is
[tex]F_y = F_{1y}+ F_{2y}[/tex]
= 0+ 4242.6N
= 4242.6N
The magnitude of the resultant force =
Using pythagorean theorm of 1243 N and 4243 N
[tex]\sqrt{(1242.6)^2 + (4242.6)^2[/tex]
[tex]\sqrt{(1544054.76) + (17999654.8)}[/tex]
[tex]\sqrt{(19543709.5)^2}[/tex]
4420.8 N
F = ma
[tex]a = \frac{F}{m}[/tex]
[tex]a =\frac{4420.8}{ 2000}[/tex]
=2.2 [tex]m/s^2[/tex]
