Finding the components of this vector

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SUMMARY

The discussion clarifies the transition from the vector representation of gravitational acceleration, denoted as \(\vec{g}\), to its scalar magnitude, represented as \(g\). Specifically, \(g\) is defined as the magnitude of the vector \(\vec{g}\), calculated using the formula \(g = |\vec{g}| = \sqrt{g_x^2 + g_y^2}\). The scalar value of gravitational acceleration is established as 9.8 m/s², which is derived from the components of gravity in the x and y directions. This distinction is crucial for understanding how vector quantities can be simplified to scalar values in physics.

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How is the vector g turning into the scalar g? What am I missing that is
allowing us to represent g as a scalar quantity and no longer a vector
quantity? When going through the algebra to find mg_x, (component
of gravity in the x-direction) I don't see how it turns into a
scalar of 9.8.

http://img124.imageshack.us/img124/3417/page00023ue.jpg
 
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When they say [itex]g[/itex] instead of [itex]\vec{g}[/itex] they mean the magnitude of [itex]\vec{g}[/itex], i.e. [itex]g=|\vec{g}| = \sqrt{g_x^2 + g_y^2}[/itex].
 

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