A duck has a mass of 2.3 kg. As the duck paddles, a force of 0.08 N acts on it in a direction due east. In addition, the current of the water exerts a force of 0.21 N in a direction of 55° south of east. When these forces begin to act, the velocity of the duck is 0.10 m/s in a direction due east. Find the magnitude and direction (relative to due east) of the displacement that the duck undergoes in 3.5 s while the forces are acting. magnitude m

direction ° south of east

Thank you for your help!

Yeah dude! that is a good question!

To find the magnitude and direction of the displacement that the duck undergoes, we can use the equations of motion. The displacement can be calculated using the equation:

Displacement (d) = Initial velocity (v0) × time (t) + 0.5 × acceleration (a) × time squared (t^2)

Since the duck is already moving with an initial velocity of 0.10 m/s due east, the initial velocity (v0) will be 0.10 m/s. The acceleration (a) is the net force divided by the mass of the duck (a = ΣF / m).

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

Net force (ΣF) = Force 1 (F1) + Force 2 (F2)

F1 = 0.08 N (due east)
F2 = 0.21 N (55° south of east)

To find the x and y components of Force 2, we need to use trigonometry. The x component (F2x) can be calculated by multiplying the magnitude of the force by the cosine of the angle:

F2x = F2 × cos(angle)
F2x = 0.21 N × cos(55°)

Similarly, the y component (F2y) can be calculated by multiplying the magnitude of the force by the sine of the angle:

F2y = F2 × sin(angle)
F2y = 0.21 N × sin(55°)

Now, we can find the net force:

ΣF = F1 + F2
ΣF = 0.08 N (due east) + F2x (west) + F2y (north)

Next, calculate the acceleration:

a = ΣF / m
a = (0.08 N + F2x - F2y) / 2.3 kg

Now, we have the acceleration value. We can substitute the given values in the displacement equation:

d = v0 × t + 0.5 × a × t^2
d = 0.10 m/s × 3.5 s + 0.5 × a × (3.5 s)^2

Finally, we can calculate the magnitude of the displacement by taking the absolute value of the result of the displacement equation. To find the direction, we can use trigonometry to find the angle of the displacement relative to due east:

Direction = tan^(-1)(final y component displacement / final x component displacement)

Plug in the values, and solve the equation to find the magnitude and direction of the displacement.