A-rocket-vertically-from-the-surface-of-the-earth-with-an-initil-velocity-v-o-show-that-its-velocity-v-at-height-h-is-given-by-v-o-2-v-2-2gh-1-h-R-where-R-is-radius-of-earth-and-g-is-the

Question Number 74411 by peter frank last updated on 24/Nov/19

A r o c k e t v e r t i c a l l y f r o m

t h e s u r f a c e o f t h e e a r t h

w i t h a n i n i t i l v e l o c i t y (v_{o})

s h o w t h a t i t s v e l o c i t y v

a t h e i g h t h i s g i v e n b y

v_{o}^{2} - v^{2} = \frac{2 g h}{1 + \frac{h}{R}}

w h e r e R i s r a d i u s o f e a r t h

a n d g i s t h e a c c e l e r a t i o n

d u e t o g r a v i t y a t t h e e a r t h

s u r f a c e

Answered by ajfour last updated on 24/Nov/19

- \frac{G M m}{R} + \frac{{m v}_{0}^{2}}{2} = - \frac{G M m}{(R + h)} + \frac{{m v}^{2}}{2}

\Rightarrow v_{0}^{2} - v^{2} = 2 (\frac{G M}{R^{2}}) R (1 - \frac{R}{R + h})

\Rightarrow v_{0}^{2} - v^{2} = \frac{2 g h}{1 + h / R} .

Commented by peter frank last updated on 24/Nov/19

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