Question

[10] (2) Consider a rocket traveling in a straight-line subject to an external force Fext acting along the same line. The equation of motion is my =-mvex + Fext where (-mvex) is the thrust. [4] (2.a) Specialize to the case of a rocket taking off vertically (from rest; and positive y is upward) in a gravitational field g, so the only external force is the weight mg. Assume that the rocket ejects mass at a constant rate, m=-k (where k is a positive constant, so that m=mo - kt). Solve the equation of motion for v as a function of t. [3] (2.b) Using the data: Vex = 3000 m/s, molm = 2, and g = 9.8 m/s2, find the space shuttle's speed two minutes into flight, assuming (what is nearly true) that it travels vertically up during this period and that g doesn't change appreciably. Compare with the corresponding result if there were no gravity. [3] (2.c) What is the thrust during the same period (if the initial mass is 2 x 10 kg) and how does it compare with the initial total weight of the shuttle (on earth)?

Answer 1

The given question is based on the concept of variable mass system or ricket propulsion.Rocket or space shuttle gains speed due to change in momentum produced by release of its mass as a exhust.

Given kan of motion müz-üven & rever a tre @ f eur -mg di m dm . akan Love or mamookt i mot indicel mang the rocker putting in the ean. mara kven-mg - an = K Ven -ga k van - g. mookt - dva k ven dat het 9 dr. Inreparing born sides , & Saw - Kven (dt - a feat at tao, Vinirical =) va kven fen moterit - If a kven en (mo - gt monks -K

mo mo 22 6 using Ven : 3000 m/s, mo an month 99.8 m/s2 tazmin = 120 sec. m Va 3000k in 2 - 9284 120 = 2079, 44 K-1176 - If there were no marity. second term will se zero v = 2079.44 K neater than velocity - in presence of gravity o aj initial man amza 2X100 kg. Thrusta anven? K veu faking valere from @ mo a oka mo at ta 120 see, no ka xx100 = 105 7x120 thrust = 10 x 3000 = 205X107 NV Initical total of of Shautle = Mog=1.96 x 107 N that is ten than jerast force. 2 moolch cec.