Question

A duck has a mass of 2.90 kg. As the duck paddles, a force of 0.120 N acts on it in a direction due east. In addition, the current of the water exerts a force of 0.200 N in a direction of 50.0° 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 2.50 s while the forces are acting. (Note that the angle will be negative in the south of east direction.)

Answer 1

here,

mass ,m = 0.29 kg

the accelration , a = net force /effective mass

a = ( 0.12 i + 0.2 * ( cos(50) i - sin(50) j)) /0.29

a = 0.86 i - 0.15 j m/s^2

the velocity of duck , v = 0.13 m/s i

time taken, t = 2.5 s

the dislacement , s = v * t + 0.5 * a * t^2

s = 0.13 i * 2.5 + 0.5 * (0.86 i - 0.15 j) * 2.5^2 m

s = 3.01 i m - 0.47 j m

the magnitude of displacement , |s| = sqrt(3.01^2 + 0.47^2) = 3.05 m

the direction , theta = arctan(0.47 /3.01) = 8.87 degree south of east