A duck has a mass of 2.70 kg. As the duck paddles, a force of 0.130 N acts on it in a direction due east. In addition, the current of the water exerts a force of 0.210 N in a direction of 52.0 ° south of east. When these forces begin to act, the velocity of the duck is 0.110 m/s in a direction due east. Find (a) the magnitude and (b) the direction (relative to due east) of the displacement that the duck undergoes in 2.70 s while the forces are acting. (Note that the angle will be negative in the south of east direction.)

Neglecting friction? I have never understood why competent teachers give problems such as this

I assume your teacher imagines there is no friction, but the current gives a force? What exactly is friction?

anyway, add the force vectors, get the resultant, then compute a=Force/mass, and assume any other friction in the water besides the current is magically not there.
Now knowing a, you can compute displacement
d=vi*t+1/2 a t^2

To find the displacement of the duck, we need to calculate the net force acting on it and then use Newton's second law of motion to find the acceleration. With the acceleration, we can then find the displacement using the equation of motion.

Given:
- Mass of the duck, m = 2.70 kg
- Force due to the paddling, F1 = 0.130 N
- Force due to the current, F2 = 0.210 N
- Angle of the current force, θ = 52.0° south of east
- Initial velocity of the duck, v0 = 0.110 m/s
- Time, t = 2.70 s

To find the net force on the duck, we need to resolve the forces into their x and y components. Since the angle θ is measured south of east, we need to consider it as negative from the east direction.

x-component of F1 = F1 * cos(0°) = 0.130 N
y-component of F1 = F1 * sin(0°) = 0 N

x-component of F2 = F2 * cos(-52.0°) = 0.210 N * cos(-52.0°)
y-component of F2 = F2 * sin(-52.0°) = 0.210 N * sin(-52.0°)

Next, we calculate the net force in the x and y directions:

Net force in the x-direction, Fnet_x = F1_x + F2_x
Net force in the y-direction, Fnet_y = F1_y + F2_y

Use Newton's second law to find acceleration:
Fnet_x = m * ax
Fnet_y = m * ay

Here, ax and ay represent the acceleration in the x and y directions, respectively.

Now, solve the equations to find the acceleration components:

ax = Fnet_x / m
ay = Fnet_y / m

Once we have the acceleration components, we can now use them to find the displacement in the x and y directions using the equation of motion:

x = x0 + v0x * t + 0.5 * ax * t^2
y = y0 + v0y * t + 0.5 * ay * t^2

Where:
- x and y are the displacements in the x-and y-directions, respectively
- x0 and y0 are the initial positions in the x-and y-directions, respectively (assumed to be zero)
- v0x and v0y are the initial velocities in the x-and y-directions, respectively.
- a x and a y are the accelerations in the x-and y-directions, respectively.

Finally, we can find the magnitude and direction of the displacement using the displacement components:

Magnitude of displacement = √(x^2 + y^2)
Direction of displacement = arctan(y / x)

Plug in the values and calculate to find the answers.