Proszę o przekształcenie wzoru by uzyskać Cały czas mi źle wychodzi.... Question from @DzikiWiewior

December 2018 2 19 Report

Proszę o przekształcenie wzoru by uzyskać $v_{2}$

$\frac{m v_{1} ^{2} }{2} - \frac{GMm}{ r_{1}} =\frac{m v_{2} ^{2}}{2} - \frac{GMm}{ r_{2}}$

Cały czas mi źle wychodzi

dominnio $\frac{m v_{1} ^{2} }{2} - \frac{GMm}{ r_{1}} =\frac{m v_{2} ^{2}}{2} - \frac{GMm}{ r_{2}}\\\\
 \frac{m v_{1} ^{2} }{2} - \frac{GMm}{ r_{1}} + \frac{GMm}{ r_{2}}=\frac{m v_{2} ^{2}}{2} \\\\
\frac{m v_{2} ^{2}}{2} = \frac{m v_{1} ^{2} }{2} - \frac{GMm}{ r_{1}} + \frac{GMm}{ r_{2}}\\\\
{v_{2} ^{2}} ={v_{1} ^{2} } - \frac{2GM}{ r_{1}} + \frac{2GM}{ r_{2}}\\\\
v_2=\sqrt{{v_{1} ^{2} } - \frac{2GM}{ r_{1}} + \frac{2GM}{ r_{2}}}$

2 votes Thanks 1

basetla $\frac{mv_1^{2}}{2}-\frac{GMm}{r_1} = \frac{mv_2^{2}}{2}-\frac{GMm}{r_2} \ \ \ \ /:m\\\\\frac{v_1^{2}}{2}-\frac{GM}{r_1}= \frac{v_2^{2}}2}-\frac{GM}{r_2}\\\\\frac{v_2^{2}}{2}=\frac{v_1^{2}}{2}+\frac{GM}{r_2}-\frac{GM}{r_1} \ \ \ \ |*2r_1r_2\\\\r_1r_2v_2^{2} = r_1r_2v_1^2}+2r_1GM-2r_2GM\\\\r_1r_2v_2^{2}=r_1r_2v_1^{2}+2GM(r_1-r_2) \ \ \ \ /:r_1r_2\\\\v_2^{2} = v_1^{2}+\frac{2GM(r_1-r_1)}{r_1r_2} \\\\v_2 = \sqrt{v_1^{2}+\frac{2GM(r_1-r_2)}{r_1r_2}}$

1 votes Thanks 1

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