Answer:
The acceleration is [tex]a = 11.88 \ m/s^2[/tex]
The velocity after 20 second is [tex]v = 267.36 \ m/s[/tex]
Explanation:
From the question we are told that
The mass of the rocket is [tex]m = 800 \ kg[/tex]
The rate of fuel consumption is [tex]r = 5 \ kg / s[/tex]
The speed of speed at which gas is ejected at atmospheric pressure is [tex]v_g = 3500 \ m/s[/tex]
Generally the thrust force (the force propelling the rocket) is mathematically represented as
[tex]F_1 = v_g * r[/tex]
=> [tex]F_1 = 3500 * 5[/tex]
=> [tex]F_1 = 17500 \ N[/tex]
Generally the net force acting on the rocket is mathematically represented as
[tex]F_{net} = F_1 - mg[/tex]
=> [tex]m * a = 17500 - (800 * 9.8)[/tex]
=> [tex]800 * a = 17500 - (800 * 9.8)[/tex]
=> [tex]a = 11.88 \ m/s^2[/tex]
Generally the rocket speed is mathematically represented as
[tex]v = v_i - gt + v_g * ln[\frac{m}{m_r} ][/tex]
Here [tex]v_i[/tex] is the initial velocity of the rocket which is 0 given that it started from rest
[tex]m_r[/tex] of the rocket after fuel has been consumed for time t = 20
second, this mathematically represented as
[tex]m_r = m - (r * t )[/tex]
=> [tex]m_r =800 - (5 * 20 )[/tex]
=> [tex]m_r = 700 \ kg[/tex]
So
[tex]v = 800 - 9.8 * 20 + 3500 * ln[\frac{800}{700} ][/tex]
=> [tex]v = 267.36 \ m/s[/tex]
