Question

2. According to Newton's Law of Universal Gravitation, the gravitational force on an object of mass m that has been projected vertically upward from Earth's surface is F( is the objer s distan boe he urfac at time t, Ris Earth's radius, ngR (x+R)2 and g is the acceleration due to gravity. Also, by Newton's Second law, mgR2 (x +R)2 dv F = mal = m dt = a. Suppose a rocket is fired vertically upward with an initial velocity vo Let h be the maximum height above the surfaced reached by the object. Show that 2g Rh dy dv hint: m b. Calculate velim vo . This limit is called escape velocity for Eartlh c. Use R-6.4 x 100 m and g 9.8 m/s2 to calculate ve in m/s dt dx

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Answer 1

a) "the sockel is fbed vertical(つ hoig above the suornce reoched by th el distomee ジニ d t and with time necod tne velbcito l us annd 0 dt- So, aud o aloe

No actodim to Nes tom's lao Solus il 2. 091 _ dス Nou whem 1a- vo om inital velocit amd Nou 09, h , tnern ~g becomes 2ero 091 clh Imnigntina both cide, we get

10 d13ニーク het ns assume, 14 hl m- 2 -2-t ! ㄨ巨 2 p.

32 | 4 Pth 9, pnoved pth ん วา 9