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183_notes:examples:momentumfast [2014/07/10 14:11] – [Solution] caballero | 183_notes:examples:momentumfast [2014/07/10 14:21] – [Solution] caballero | ||
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$$|\vec{v}| = \sqrt{v_x^2+v_y^2+v_z^2} = \sqrt{(-2.05\times10^7 \dfrac{m}{s})^2+(6.02\times10^7 \dfrac{m}{s})^2+(0)^2} = 6.36 \times 10^7 \dfrac{m}{s}$$ | $$|\vec{v}| = \sqrt{v_x^2+v_y^2+v_z^2} = \sqrt{(-2.05\times10^7 \dfrac{m}{s})^2+(6.02\times10^7 \dfrac{m}{s})^2+(0)^2} = 6.36 \times 10^7 \dfrac{m}{s}$$ | ||
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+ | Next, we compute the gamma factor. | ||
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+ | $$\gamma = \dfrac{1}{\sqrt{1-\left(\dfrac{|\vec{v}|}{c}\right)^2}} = \dfrac{1}{\sqrt{1-\left(\dfrac{6.36 \times 10^7 \dfrac{m}{s}}{3.00 \times 10^8 \dfrac{m}{s}}\right)^2}} = \dfrac{1}{\sqrt{1-(0.212)^2}}=1.02$$ | ||
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+ | Finally, we compute the momentum vector. | ||
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+ | $$\vec{p} = \gamma m \vec{v} = (1.02) (9.11\times10^{-31} kg) \langle -2.05\times10^7, | ||
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