Question

A duck has a mass of 2.70 kg. As the duck paddles, a force of 0.110 N acts on it in a direction due east. In addition, the current of the water exerts a force of 0.220 N in a direction of 47.0° 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 2.70 s while the forces are acting. (Note that the angle will be negative in the south of east direction.)

Answer 1

a) The magnitude will be 0.838m

b) The displacement will be -17.35°

What is displacement?

The path covered by an object from its initial point to final point.

Forces acting on the duck

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

X = Vox * t + ax/2 * t²

X = 0.12* 3.2 + 0.0813/2*3.2²

X = 0.8

The displacement on the y-axis:

Y = Voy * t + ay/2 * t²

X = 0 - 0.0491/2*3.2²

Y=-0.25m

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

0.838m  at an angle of -17.35°

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