A duck has a mass of 2.8 kg. As the duck paddles, a force of 0.05 N acts on it in a direction due east.

In addition, the current of the water exerts a force of 0.15 N in a direction of 60° south of east.
When these forces begin to act, the velocity of the duck is 0.12 m/s in a direction due east.

Find the magnitude and direction (relative to due east) of the displacement that the duck undergoes in 2.2 s while the forces are acting

Draw a diagram of the forces. By the law of cosines, the resultant force is

f^2 = .05^2 + .15^2 - 2(.05)(.15)cos120°
f = 0.18N in the direction θ where
tanθ = -.15*√3/2 / .125
θ = -46° or, E46°S

Since F = ma, a = .125i - .13j

s = .5 at^2
= .5(.125i - .13j)*2.2^2
= 2.42(.125i - .13j)
= .3025i - .3146j
|s| = 0.436m

To find the displacement of the duck in 2.2 seconds while the forces are acting, we need to use Newton's second law of motion:

F = m * a

Where F is the net force acting on the duck (the vector sum of the two forces), m is the mass of the duck, and a is the acceleration of the duck.

First, let's find the net force acting on the duck:

Net force = Force 1 + Force 2

Force 1 is the force acting on the duck due east, which has a magnitude of 0.05 N and is in the direction due east.

Force 2 is the force acting on the duck due to the water current, which has a magnitude of 0.15 N and is in a direction 60° south of east. To find the x and y components of this force, we can use trigonometry:

Force 2x = Force 2 * cos(60°)
Force 2y = Force 2 * sin(60°)

Now, let's calculate the x and y components of the net force:

Net force x = Force 1 + Force 2x
Net force y = Force 2y

Next, we can use Newton's second law to find the acceleration of the duck:

a = Net force / m

Once we have the acceleration, we can use the kinematic equation to find the displacement of the duck:

s = ut + (1/2)at^2

Where s is the displacement, u is the initial velocity, t is the time, and a is the acceleration.

Given that the initial velocity of the duck is 0.12 m/s due east, the time is 2.2 seconds, and the mass of the duck is 2.8 kg, we can substitute these values into the equation to find the displacement.

Finally, we can find the magnitude and direction of the displacement by calculating the magnitude using the Pythagorean theorem:

Magnitude = sqrt(displacement x^2 + displacement y^2)

And the direction can be found using the inverse tangent:

Direction = arctan(displacement y / displacement x)

By following these steps, we can find the magnitude and direction of the displacement that the duck undergoes in 2.2 seconds while the forces are acting.