A duck has a mass of 2.4 kg. As the duck paddles, a force of 0.06 N acts on it i

Question

A duck has a mass of 2.4 kg. As the duck paddles, a force of 0.06 N acts on it in a direction due east. In addition, the current of the water exerts a force of 0.23 N in a direction of 50° south of east. When these forces begin to act, the velocity of the duck is 0.11 m/s in a direction due east. Find the magnitude and direction (relative to due east) of the displacement that the duck undergoes in 2.2 s while the forces are acting.

Explanation / Answer

Resolve all awkward(those at an angle to some axis) forces into rectangular components. Thus we have the forces -: F(duck) = 0.06N east. F(water) = 0.23N 50° south of east. F(bouyant) = In a direction upwards, equal to the sum of the forces acting down. F(weight) = m * g = 2.4 * 10 = 24N Break F(water) into two forces, F(down) and F(east) as per resolution methods. F(down) = F(water) sin50 = 0.23 * 0.766 = 0.176 N F(east) = F(water) cos50 = 0.23 * cos50° = 0.148 N After resolution, form force equations. F(bouyant) = F(weight) + F(down) = 24 + 0.176 = 24.176 N This force is inconsequential to our calculations. We need the forces causing the motion of the duck. Those are F(duck) + F(east) = m * a => 0.0 6+ 0.148 = 2.4 * a => 0.208 = 2.4 * a => a = 0.086 m/s^2 east. (east direction is +ve, west is -ve). This is the net acceleration of the duck. Now we apply an equation of motion to finish it. v = u + at Here u = 0 m/s (duck starts from rest) a = 0.086 m/s^2 t = 2.2s v = ? v = 0.086 * 2.2 = 0.191 m/s approx in the east direction.

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