Question

A rocket takes off from Earth and reaches a speed of 105 m/s in 18.0 s. If the exhaust speed is 1,200 m/sand the mass of fuel burned is 110 kg, what was the initial mass (in kg, including the initial fuel) of the rocket?

Answer 1

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,

$v=u\ ln(\dfrac{m_{i}}{m})-gt$....(I)

We know that,

$m=m_{i}-m_{bf}$

Put the value of m in equation (I)

$v=u\ ln(\dfrac{m_{i}}{m_{i}-m_{bf}})-gt$

$m_{i}=\dfrac{m_{bf}}{1-e^-{\dfrac{v+gt}{u}}}$

$m_{i}=\dfrac{110}{1- e^-{\frac{105+9.8\times18}{1200}}}$

$m_{i}=526.2 kg$

Hence, The initial mass of the rocket is 526.2 kg.