A rockets mass decreases as it burns fuel The equation of motion for a rocket in vertical flight can be obtained from Newton s law and is where T is the rockets thrust and its mass as a function of time is given by m(t) m 0 (1 rt b) The rockets initial mass is m 0 , the burn time is b, and r is the fraction of the total mass accounted for by the fuel Use the values T 48 000 N, m 0 2200 kg, r 0 8, g 9 81 m s 2 , and b 40 s a Use MuPAD to compute the rockets velocity as a function of time for t b b Use MuPAD to compute the rockets velocity at burnout dv m(t) T m(t)g dt

Question: A rockets mass decreases as it burns fuel. The equation of motion for a rocket in vertical flight can be obtained from Newton s law

A rocket’s mass decreases as it burns fuel. The equation of motion for a rocket in vertical flight can be obtained from Newton’ s law and is

dv m(t) = T – m(t)g dt

where T is the rocket’s thrust and its mass as a function of time is given by m(t) = m₀(1 - rt/b). The rocket’s initial mass is m₀, the burn time is b, and r is the fraction of the total mass accounted for by the fuel. Use the values T = 48 000 N, m₀ = 2200 kg, r = 0.8, g = 9.81 m/s², and b = 40 s.

a. Use MuPAD to compute the rocket’s velocity as a function of time for t ≤ b.

b. Use MuPAD to compute the rocket’s velocity at burnout.

dv m(t) = T m(t)g dt

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