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# Find the escape velocity $v_0$ that is needed to propel a rocket of mass $m$ out of the gravitational field of a planet with mass $M$ and radius $R$. Use Newton's Law of Gravitation (see Exercise 6.4.33) and the fact that the initial kinetic energy of $\frac{1}{2} mv^2_0$ supplies the needed work.

## $v_{0}=\sqrt{\frac{2 G M}{R}}$

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Integration Techniques

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the problem is finding escape. We lasted with zero that is needed to propel a rocket of mice Ham a tough the gravitational field off planet of this mask after AM and riders are youth. Newton's law of gravitation and the fact that the initial matic energy off half on with their squire supplies that major work. The first using Newton's slough off gravitation half ofwork made it if they caught you improper, integral from Capt Awar infinity. She have on and over square. Yeah, it should be equal to one half. I'm with Cyril. Squire. We need to find zero the first this improper, Integral. If they caught you, Um um limit a ghost penetrated into grow from capt. Our tow A one over X square. Yes, this is it on lim A cost Vanity one over. Negative one over a wan ho har. This is the captain tree. We are. So we have one half. Um, wait. Zero square. It's the call to G. Over. We can start on you. So we're half read. Zero squire, Shoot house t. Um, For what

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