Question

A rocket is launched from the Earth’s surface. Unfortunately, the engineers have miscalculated and the rocket runs out of fuel when its height is exactly one earth radii above the earth’s surface. The rocket immediately falls from rest back to toward the surface. Ignore friction and air resistance in your calculations. R subscript E equals 6.37 cross times 10 to the power of 6 space m e t e r s comma space M subscript E equals 5.98 cross times 10 to the power of 24 space k g comma space G space equals space 6.67 cross times 10 to the power of negative 11 end exponent N fraction numerator m squared over denominator k g squared end fraction falling to earth from earth radii height (a) Determine the gravitational potential energy of the rocket when it's at the maximum height above the surface. (b) Calculate the work done by gravity as the rocket falls back to the surface of the earth. (c) Determine the speed of the rocket when it impacts the surface.

Answer 1

Uat "X 2x 6.378106 where m= J 39.8866m x 103 solution ca) GM EM at maximum height QRE 6067 x 10-9 x 5: 98x1624 J 12.74 x 106 J 3:1308 x 107) m mars al rocket in kg 3:1308x107 m) Lb) -GMEM RE =-2* 3.1308X10 3x107m) J = (-6.2616x107m) so W = Work come by gravity at maximum height - Uat surface (34308 X107')-(-62616x10m) 3.13088 107m I 3. 1308x107m ! I (c) from work -energy Theorem 3113088107m m15 V 2x3.1308X107 7.913 x 10 7,913 x 103 mis U at at surface V2 “Sm let 介 3 m/s