# A 23.9 kg mass has a 3i-2jm/s velocity and a 21.3 kg mass has a 3i-10jm/s velocity. What is the magnitude of the total momentum of the two masses?

Feb 15, 2018

$\text{please have a look at the fallowing details.}$

#### Explanation:

${\vec{P}}_{1} = {m}_{1} \cdot {\vec{v}}_{1}$

${\vec{P}}_{1} = 23.9 \cdot \left(3 i - 2 j\right) = 71.7 i - 47.8 j$

${\vec{P}}_{2} = {m}_{2} \cdot {\vec{v}}_{2}$

${\vec{P}}_{2} = 21.3 \left(3 i - 10 j\right) = 63.9 i - 213 j$

$\Sigma \vec{P} = {\vec{P}}_{1} + {\vec{P}}_{2}$

$\Sigma \vec{P} = 71.7 i + 63.9 i + \left(- 47.8 j - 213 j\right)$

$\Sigma \vec{P} = 135.6 i - 260.8 j \text{ total momentum vector}$

$P = \sqrt{{\left(135.6\right)}^{2} + {\left(- 260.8\right)}^{2}} \text{ magnitude}$

$P = \sqrt{18387.36 + 68016.64}$

$P = 293.95 k g \text{ } \cdot m {s}^{-} 1$