Answer:
The initial mass of the rocket is 526.2 kg.
Explanation:
Given that,
Final speed = 105 m/s
Time = 18.0 s
Exhaust initial speed = 1200 m/s
Mass of burned fuel = 110 kg
We need to calculate the initial mass
The velocity change of rocket under gravity is defined as,
[tex]v=u\ ln(\dfrac{m_{i}}{m})-gt[/tex]....(I)
We know that,
[tex]m=m_{i}-m_{bf}[/tex]
Put the value of m in equation (I)
[tex]v=u\ ln(\dfrac{m_{i}}{m_{i}-m_{bf}})-gt[/tex]
[tex]m_{i}=\dfrac{m_{bf}}{1-e^-{\dfrac{v+gt}{u}}}[/tex]
[tex]m_{i}=\dfrac{110}{1- e^-{\frac{105+9.8\times18}{1200}}}[/tex]
[tex]m_{i}=526.2 kg[/tex]
Hence, The initial mass of the rocket is 526.2 kg.
The initial mass of the rocket including the initial fuel is 1257.14 kg.
The initial mass of the rocket is determined by applying the principle of conservation of linear momentum as follows;
m₁v₁ = m₂v₂
105m = 1200 x 110
105 m = 132,000
m = 132,000/105
m = 1257.14 kg
Thus, the initial mass of the rocket including the initial fuel is 1257.14 kg.
Learn more about conservation of linear momentum here: https://brainly.com/question/7538238
