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Question Number 170284 by sciencestudent last updated on 19/May/22

Commented by sciencestudent last updated on 19/May/22

$A f o o t b a l l p l a y e r w e i g h i n g 200 L b f l i e s$ $u p t o 7 m i l e s i n a p l a n e a c c o r d i n g t o$ $t h e f i g u r e a b o v e, s o h o w m u c h w e i g h t$ $d o e s a f o o t b a l l p l a y e r l o s e ?$
Commented by sciencestudent last updated on 19/May/22

$s o r r y t h i s i s a i r p l a n e .$
Commented by sciencestudent last updated on 19/May/22

$B u t t h e r a d i u s o f e a r t h i s 6.4 \cdot 10^{6} m$ $3960 k m i s w r o n g .$
Commented by mr W last updated on 20/May/22

$R = 3960 m i l e s, n o t 3960 k m!$
Commented by mr W last updated on 20/May/22

$i f t h e w e i g h t o f a m a n o n t h e s u r f a c e$ $o f e a r t h i s W, a n d i t s w e i g h t a t a$ $h e i g h t h i s W_{h}, t h e n$ $W = \frac{G M m}{R^{2}}$ $W_{h} = \frac{G M m}{{(R + h)}^{2}}$ $w e g e t :$ $W_{h} = {(\frac{R}{R + h})}^{2} W < W$ $t h e w e i g h t h e l o s e s a t h e i g h t h i s$ $Δ W = W - W_{h} = [1 - {(\frac{R}{R + h})}^{2}] W$ $= [1 - {(\frac{3960}{3960 + 7})}^{2}] \times 200 = 0.705 l b$
Commented by Tawa11 last updated on 08/Oct/22

$Great sir$
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