A duck has a mass of 2.90 kg. As the duck paddles, a force of 0.110 N acts on it

Question

A duck has a mass of 2.90 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 0.180 N in a direction of 51.0 ° south of east. When these forces begin to act, the velocity of the duck is 0.130 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 2.20 s while the forces are acting. (Note that the angle will be negative in the south of east direction.)

Explanation / Answer

Given that mass of duck m =2.90 kg Force F1 = (0.110 N)i F2 = (0.180 N)cos51 i - (0.180 N)sin51 j = (0.113277) i -(0.139886) j ------------------------------------------------------------------- The net force acting on duck is F = F1+ F2 = (0.223277) i - (0.139886) j The acceleration of the duck is a = F/m = ((0.223277) i - (0.139886) j)/(2.90 kg) = (0.077)i- (0.0482) j From the kinematic relations s = u t + (1/2)at^2 = (0.130 i)(2.20) + (0.5)((0.077)i- (0.0482) j)(2.20)^2 = 0.286 i + 0.0385 i - 0.233288 j = 0.3245 i - 0.233288 j The mangitude of the displacement is s=0.39965 m Direction               f =tan-1[- 0.233288 / 0.3245 ] = -35.7129o

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