A duck has a mass of 2.9 kg. As the duck paddles, a force of 0.07 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 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 2.7 s while the forces are acting. How do you get the direction?

there is absolutely no way its that complicated. and at points it looks like you made up some values. be more clear.

f = ma,

0.07 = 2.9a,
a = 0.07/2.9 = 0.024 m/s^2,
d1 = Vo*t + 0.5*at^2,
= 0.12*2.7 + 0.5*0.024*(2.7)^2,
= 0.3481 + 0.0880 = 0.4361 m., E.

0.21 = 2.9a,
a = 0.21 / 2.9 = 0.0724 m/s^2,
d2 = 0.12*2.7 + 0.5*0.0724*(2.7)^2,
= 0.3481 + 0.2639 = 0.6120 m.@ 60
deg S. of E. = 300 CCW.

RESULTANT(R)

X = hor = 0.4361 + 0.6120*cos300,
= 0.4361 + 0.306 = 0.7421 m.

Y = ver = 0 + 0.6120*sin300 = -0.530m

tanA = y/x = -0.5300 / 0.7421 = -0.7142
A = -35.5 deg = 35.5 deg S.of E. = 324.5 deg CCW.

R = X + iY = 0.7421 - i0.5300

R = X / cosA = 0.7421 / cos324.5 = 0.9115 m @ 35.5 deg. S.of W.

DISPLACEMENT(D)

D = R - Vo*t,
= (0.7421 - i0.5300) - 0.12*2.7
= 0.7421 - 0.324 - i5300,
= 0.4181 - i0.5300,

tanB = Y / X = -0.5300/0.4181=-1.268,
B = -51.7 Deg = 308.3 deg CCW.

Magnitude = x / cosB = 0.4181 / cos308.3 = 0.6751 m.

Direction = 51.7 deg S. of E.

To find the magnitude and direction of the displacement undergone by the duck, we can use Newton's second law of motion, which states that the net force acting on an object is equal to its mass times its acceleration.

1. First, let's find the net force acting on the duck. We can do this by adding the individual forces acting on it.
Net force = Force due east + Force 60° south of east

2. To find the acceleration of the duck, we can divide the net force by its mass.
Acceleration = Net force / Mass

3. Once we have the acceleration, we can use the kinematic equation to calculate the displacement of the duck.
Displacement = Initial velocity * Time + (1/2) * Acceleration * Time^2

4. Finally, to determine the direction, we can use trigonometry. We can use the fact that the displacement in the east direction is equal to the magnitude of displacement times the cosine of the angle between displacement and due east.
East displacement = Displacement * cos(angle)

Now, let's calculate the magnitude and direction of displacement step by step:

Given:
Mass (m) = 2.9 kg
Force due east = 0.07 N
Force 60° south of east = 0.21 N
Initial velocity (v) = 0.12 m/s
Time (t) = 2.7 s

Step 1: Calculate the net force acting on the duck.
Net force = 0.07 N + 0.21 N = 0.28 N

Step 2: Calculate the acceleration of the duck.
Acceleration = Net force / Mass
Acceleration = 0.28 N / 2.9 kg

Step 3: Calculate the displacement of the duck.
Displacement = Initial velocity * Time + (1/2) * Acceleration * Time^2

Step 4: Calculate the east displacement.
East displacement = Displacement * cos(angle)

To find the angle, we know that its direction is 60° south of east. So, the angle between the displacement vector and due east would be (180° - 60°) = 120°.

Finally, substitute the given values and calculate the magnitude and direction of displacement using the above equations.

To find the magnitude and direction of the displacement that the duck undergoes, we can use the laws of physics, specifically the principles of vector addition. The displacement is the change in position of an object, and it can be represented as a vector quantity that has both magnitude and direction.

Here is how you can solve the problem step by step:

1. Consider the forces acting on the duck: the force from paddling (0.07 N in the east direction) and the force from the water current (0.21 N at a 60° south of east angle).

2. Find the net force acting on the duck by adding the components of the two forces. Break down each force into east and north components using trigonometry.
For the force from paddling: East component = 0.07 N * cos(0°) (Since it is in the east direction)
North component = 0.07 N * sin(0°) (Since there is no north component)

For the force from water current: East component = 0.21 N * cos(60°)
North component = 0.21 N * sin(60°)

Add the east and north components of the forces together to find the net force in each direction.

3. Calculate the acceleration of the duck using Newton's second law: F = ma
Since we know the net force and the mass, rearrange the equation to solve for acceleration.

4. Use the initial velocity, acceleration, and time to find the final velocity of the duck using the equation of motion: v = u + at
u = initial velocity (0.12 m/s in the east direction)
a = acceleration (found in step 3)
t = time (2.7 s)

5. Calculate the displacement of the duck using average velocity and time: s = (u + v)/2 * t
u = initial velocity (0.12 m/s in the east direction)
v = final velocity (found in step 4)
t = time (2.7 s)

6. Finally, find the magnitude and direction of the displacement. The magnitude is the absolute value of the displacement vector, and the direction is given as an angle relative to due east.

To get the direction of the displacement relative to due east, you can use trigonometry. The direction can be found by taking the inverse tangent of the north component over the east component. This will give you the angle relative to due east.

By following these steps and performing the necessary calculations, you can find both the magnitude and direction of the displacement that the duck undergoes in 2.7 seconds.