Answer:
a) The x and y components of the momentum are
and
, 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:
(1)
Where:
- Vector momentum, measured in kilogram-meters per second.
- Mass of the particle, measured in kilograms.
- Vector velocity, measured in meters per second.
If we know that
and
, then the momentum is:
![\vec p = (2.93)\cdot (2.98\,\hat{i}-3.98\,\hat{j})\,\,\,\left[\frac{kg\cdot m}{s} \right]](https://tex.z-dn.net/?f=%5Cvec%20p%20%3D%20%282.93%29%5Ccdot%20%282.98%5C%2C%5Chat%7Bi%7D-3.98%5C%2C%5Chat%7Bj%7D%29%5C%2C%5C%2C%5C%2C%5Cleft%5B%5Cfrac%7Bkg%5Ccdot%20m%7D%7Bs%7D%20%5Cright%5D)
![\vec p = 8.731\,\hat{i}-11.661\,\hat{j}\,\,\,\left[\frac{kg\cdot m}{s} \right]](https://tex.z-dn.net/?f=%5Cvec%20p%20%3D%208.731%5C%2C%5Chat%7Bi%7D-11.661%5C%2C%5Chat%7Bj%7D%5C%2C%5C%2C%5C%2C%5Cleft%5B%5Cfrac%7Bkg%5Ccdot%20m%7D%7Bs%7D%20%5Cright%5D)
The x and y components of the momentum are
and
, respectively.
b) The magnitude and direction of momentum are represented by the following expressions:
(2)
(3)
Where:
- Magnitude of momentum, measured in kilogram-meters per second.
- Direction of momentum, measured in sexagesimal degrees.
If we know that
and
, then the magnitude and direction of momentum are, respectively:




The magnitude and direction of its momentum are approximately 14.567 kilogram-meters per second and 306.823º.