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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 0.160 N in a direction of 56.0° south of east. When these forces begin to act, the velocity of the duck is 0.120 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 3.20 s while the forces are acting. (Note that the angle will be negative in the south of east direction.)

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lcmendozaf

Answer:

a) 0.838m

b) -17.35°

Explanation:

Forces acting on the duck are:

x-axis:    0.13 + 0.16*cos(-56°) = 2.7 * ax   =>    ax = 0.0813 m/s^2

y-axis:    0.13*sin(-56°) = 2.7 * ay              =>     ay = -0.0491 m/s^2

The displacement on the x-axis:

[tex]X = Vox*t+ax/2*t^2=0.12*3.2 + 0.0813/2*3.2^2[/tex]

X=0.8m

The displacement on the y-axis:

[tex]Y = Voy*t+ay/2*t^2=0 - 0.0491/2*3.2^2[/tex]

Y=-0.25m

Now, the magnitude and angle of this displacement [0.8,-0.25] is:

0.838m  at an angle of -17.35°

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