To find the initial mass of the rocket, you can use the principle of conservation of momentum. The momentum of the rocket before and after it takes off must be equal. The momentum of the rocket can be calculated as the product of its mass and velocity.
Before takeoff, the rocket is at rest, so its initial momentum is 0. After taking off, the rocket reaches a speed of 125 m/s. Let's denote the initial mass of the rocket as M (in kg), and the mass of fuel burned as m (in kg).
The momentum of the rocket after takeoff is given by: M * 125 m/s
The momentum of the expelled fuel can be calculated as the product of the mass of fuel burned (m) and the exhaust speed (1,520 m/s): m * 1520 m/s
According to the conservation of momentum, the initial momentum (0) must be equal to the total momentum after takeoff. Therefore, we can write the equation as:
0 = M * 125 m/s - m * 1520 m/s
Now, let's solve for M, the initial mass of the rocket:
0 = 125M - 1520m
We also know that the mass of fuel burned is given as 114 kg, so m = 114 kg.
0 = 125M - 1520 * 114
Now, let's solve for M:
0 = 125M - 173280
125M = 173280
M = 173280 / 125
M ≈ 1386.24 kg
So, the initial mass of the rocket was approximately 1386.24 kg.
