# Answer to Question #118509 in Mechanics | Relativity for Amanda

Question #118509
A 9.00 kg object, travelling South with a speed of 8.50 m/s, is moving towards a 12.0 kg
object that is moving East with a speed of 6.00 m/s. Determine the total momentum
1
2020-05-28T12:02:36-0400

The total momentum is the vector sum of all momenta. Assume that y-axis points northward, y-axis looks eastward:

"\\vec{p}_x=\\sum^n_{i=1} m_i\\vec{v}_{xi}=12\\cdot6=72\\text{ kg}\\cdot\\text{m\/s},\\\\\n\\space\\\\\n\\vec{p}_y=\\sum^n_{i=1} m_i\\vec{v}_{yi}=9\\cdot(-8.5)=-76.5\\text{ kg}\\cdot\\text{m\/s}."

We can find the magnitude of the total momentum:

"p=\\sqrt{p_x^2+p_y^2}=\\sqrt{72^2+(-76.5)^2}=105\\text{ kg}\\cdot\\text{m\/s}."

The angle above x-axis (north of east) is

"\\theta=\\text{atan}\\frac{\\vec{p_y}}{\\vec{p_x}}=-46.7^\\circ,"

or 46.7° below x-axis (below east axis), or 46.7° south of east.

Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!