Question

A duck has a mass of 2.90 kg. While paddling, it experiences a force of 0.250 N at an angle of 55.0° south of east. Initially, the duck moves at 0.150 m/s due east. Calculate:

(a) the magnitude
(b) the direction (relative to due east) of the displacement that the duck undergoes in 2.10 seconds with the given forces acting. ​

Answer 1

To calculate the displacement of the duck, we need to find the net force acting on it and the acceleration of the duck. Finally, we can use the kinematic equation to calculate the displacement.

Step-by-step explanation:

To calculate the displacement of the duck, we need to find the net force acting on it. The given force of 0.250 N at an angle of 55.0° south of east can be broken down into its east and south components. The east component (Fx) can be found using the formula Fx = F * cos(θ), where θ is the angle. So in this case, Fx = 0.250 N * cos(55.0°).

Next, we need to find the acceleration of the duck using Newton's second law, F = m * a. Rearranging the equation, we have a = F / m. Plugging in the values, we get a = 0.250 N / 2.90 kg.

Finally, we can use the kinematic equation, d = v0 * t + 0.5 * a * t^2, to calculate the displacement. Plugging in the values, we get d = (0.150 m/s) * 2.10 s + 0.5 * (0.250 N / 2.90 kg) * (2.10 s)^2.