Question

Question 6 Zero, a hypothetical planet, has a mass of 4.2 x 1023 kg, a radius of 2.9 x 106m, and no atmosphere. A 10 kg space probe is to be launched vertically from its surface. (a) If the probe is launched with an initial kinetic energy of 5.0 x 10?), what will be its kinetic energy when it is 4.0 x 106 m from the center of Zero? (b) If the probe is to achieve a maximum distance of 8.0 x 106 m from the center of Zero, with what initial kinetic energy must it be launched from the surface of Zero? (a) Number: Units: (b) Number: Units:

Answer 1

1823 ng mass Radius of served Law Energy - Ef Keft C G mm me 4.28 105 kg Given of ny potuerteal plomet ms 4.2x18 of promet (R4 2:9 x106m Groanifational mai Poree is a conseymaline fonce. Thus, the mechanical eney gy the probe and planet will be cone So, from from the of conservation of Kilit ; = KEL + PEL GIMM Ri Rf KÊ;KEL: (6: Mm. Gemma Rf A. KES = KE:- Goma como P promet Ris Radius of the planet Rfe Redines distance of probe from centre of from equation ③ substituting ki, 5*10*1 G = 6.6 7x10 11 Nimzinga m= lokg Ri= 2.9x106m Rf = 4x100m Ri M = mass wheye 0 ma mass Jof proobe heyo. R.E.P = (5x704- 8,67x17') x 4.2622 10 2.9 106 + 6-67*15114846281023x10 4x106 2.34 1077 If the probe achieve a maximum distance of Sixto 8x 100 m from centre of zeyon As the probe reaches the maximum disromeeIts final speed will be zeyo, so its final kinette eneroy at from equation ® 0 = KÊi - Gymmacher - kop) ay & Eie (kr - kf) • 6167x1511x14.200 1023410A Gimm, 2.9x100 Bone) 6:16*707 so Iniffal kinetic energy the proobe must be Golba not Scanned with CamScanner