Question

78. A rocket takes off from Earth and reaches a speed of 100 m/s in 10.0 s. If the exhaust

speed is 1500 m/s and the mass of fuel burned is 100 kg, what was the initial mass of the rocket?

Answer 1

5866.9 kg

Step-by-step explanation:

We can use the conservation of momentum to solve this problem. The momentum of the rocket and fuel system is conserved, so:

Initial momentum = Final momentum

The initial momentum of the system is zero since the rocket is at rest initially. The final momentum is the momentum of the rocket after burning the fuel. We can find the final momentum using the rocket equation:

Δv = ve * ln(m0 / mf)

where Δv is the change in velocity (100 m/s), ve is the exhaust speed (1500 m/s), m0 is the initial mass of the rocket and fuel system (what we want to find), and mf is the final mass of the rocket and fuel system (m0 - 100 kg).

Solving for m0, we get:

m0 = mf * exp(Δv / ve) = (m0 - 100 kg) * exp(100 / 1500)

Simplifying this equation, we get:

m0 = 100 kg / (1 - exp(100 / 1500))

m0 = 5866.9 kg (rounded to four significant figures)

Therefore, the initial mass of the rocket and fuel system was approximately 5866.9 kg.