A duck has a mass of 2.30 kg. As the duck paddles, a force of 0.110 N acts on it
ID: 1984187 • Letter: A
Question
A duck has a mass of 2.30 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 0.170 N in a direction of 49.0 ° south of east. When these forces begin to act, the velocity of the duck is 0.100 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 3.10 s while the forces are acting. (Note that the angle will be negative in the south of east direction.)I have not been able to reach the correct answer yet can someone please help me. I am not sure where I am going wrong.
Explanation / Answer
Fnet = 0.110i + 0.170cos49 - 0.170sin49 j N
Fnet = 0.222i - 0.128j N
a = F / m = 0.222i - 0.128 j / 2.3 = 0.0965i - 0.0556 j m/s2
s = ut + at2 /2
s = 0.1i X 3.1 + (0.0965i - 0.0556 j ) x 3.12 /2 = 0.774i - 0.267j m
a) magnitude |s| = 0.7742 + 0.2672 = 0.819 m
b) direction = tan-1 (0.267 / 0.774) = 19.03 degrees south of east.