A space vehicle in gravity-free and drag free outer space launches a smaller spa

Question

A space vehicle in gravity-free and drag free outer space launches a smaller spacecrat ints a meteor shower region. The 2-kg sensitive instrument package of this spacecrant total mass) limits the maximum acceleration to no more than 40 m/sec It solid propellant rocket motor (specific impulse Isp=250 sec andpropela (1) Determine the maximum allowable burn time, assuming steady constant prope mass flow; (2) is launched by a lant Determine the maximum velocity relative to the launch vehicle. 25 -3101

Explanation / Answer

Given that,

M = 25 kg

a = 40 m/s2

Impulse = 250 s

a) Burn time = ?

     we know that,

F = ma

     = 20 x 40

     = 800 N

Isp = F / m0 g

     250 = 800 / m0 x 10

     m0 = 800 / 2500

        = 0.32

m0 = m /t

t = m/m0

    = 25 / 0.32

    = 78 s

V = u + at

initial velocity , u = 0

V = 40 x 78

V = 3120 m/s

           

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