Question

a rocket of mass 40kg has 160 kg fuel.the exhaust velocity of the fuel is 2km/s.the rate of consumption of fuel is 4kg/s.calculate the ultimate velocity speed gained by the rocket.

Answer 1

Answer:

=> The ultimate vertical speed gained by the rocket:

v = u - gt + v_r * Ln (m./m)

=>Here, the fuel will be zero when we consider the ultimate speed.

Thus, mass of rocket, m = 40 kg

Initial mass (mass of rocket + mass of fuel) m. = 40kg + 160kg = 200kg

Exhaust velocity of the fuel, v_r = 2 km / s = 2 * 10^3 m/s

Rate of consumption of fuel, μ = (-dm/dt) = 4 kg/s

the time taken to utilize all fuel, t = 160 / 4 = 40s

Here, u = 0

g = 10 m/s^2

=> Therefore, v = 0 - 10 * 40 + 2 * 10^3 Ln (200/40)

v = (-400 + 2000 Ln 5) m/s

v = -400 + 3219 m/s

v = 2819 m/s

v = 2.82 km/s

Thus,  the ultimate  vertical speed gained by the rocket is 2.82 km/s.