Answer:
a) The x and y components of the momentum are [tex]8.731\,\frac{kg\cdot m}{s}[/tex] and [tex]-11.661\,\frac{kg\cdot m}{s}[/tex], respectively.
b) The magnitude and direction of its momentum are approximately 14.567 kilogram-meters per second and 306.823º.
Explanation:
a) The vectorial equation of momentum is represented by the following expression:
[tex]\vec p = m\cdot \vec v[/tex] (1)
Where:
[tex]\vec p[/tex] - Vector momentum, measured in kilogram-meters per second.
[tex]m[/tex] - Mass of the particle, measured in kilograms.
[tex]\vec v[/tex] - Vector velocity, measured in meters per second.
If we know that [tex]m = 2.93\,kg[/tex] and [tex]\vec v = 2.98\,\hat{i}-3.98\,\hat{j}\,\,\,\left[\frac{m}{s} \right][/tex], then the momentum is:
[tex]\vec p = (2.93)\cdot (2.98\,\hat{i}-3.98\,\hat{j})\,\,\,\left[\frac{kg\cdot m}{s} \right][/tex]
[tex]\vec p = 8.731\,\hat{i}-11.661\,\hat{j}\,\,\,\left[\frac{kg\cdot m}{s} \right][/tex]
The x and y components of the momentum are [tex]8.731\,\frac{kg\cdot m}{s}[/tex] and [tex]-11.661\,\frac{kg\cdot m}{s}[/tex], respectively.
b) The magnitude and direction of momentum are represented by the following expressions:
[tex]\|\vec p \| = \sqrt{p_{x}^{2}+p_{y}^{2}}[/tex] (2)
[tex]\theta = \tan^{-1}\left(\frac{p_{y}}{p_{x}} \right)[/tex] (3)
Where:
[tex]\|\vec p\|[/tex] - Magnitude of momentum, measured in kilogram-meters per second.
[tex]\theta[/tex] - Direction of momentum, measured in sexagesimal degrees.
If we know that [tex]p_{x} = 8.731\,\frac{kg\cdot m}{s}[/tex] and [tex]p_{y} = -11.661\,\frac{kg\cdot m}{s}[/tex], then the magnitude and direction of momentum are, respectively:
[tex]\|\vec p\| = \sqrt{\left(8.731\,\frac{kg\cdot m}{s} \right)^{2}+\left(-11.661\,\frac{kg\cdot m}{s} \right)^{2}}[/tex]
[tex]\|\vec p\| \approx 14.567\,\frac{kg\cdot m}{s}[/tex]
[tex]\theta =\tan^{-1}\left(\frac{-11.661\,\frac{kg\cdot m}{s} }{8.731\,\frac{kg\cdot m}{s} } \right)[/tex]
[tex]\theta \approx 306.823^{\circ}[/tex]
The magnitude and direction of its momentum are approximately 14.567 kilogram-meters per second and 306.823º.
