A 4.40-kg model rocket is launched, shooting 53.0 g of burned fuel from its exhaust at an average velocity of 650 m/s. What is the velocity of the rocket after the fuel has burned? (Ignore effects of gravity and air resistance.)

To find the velocity of the rocket after the fuel has burned, we can use the principle of conservation of momentum. The initial momentum of the rocket and fuel system should be equal to the final momentum of the rocket after the fuel has been expelled.

The momentum of an object can be calculated by multiplying its mass by its velocity. So, let's begin by finding the initial momentum of the rocket and fuel system.

Initial momentum = (mass of rocket + mass of fuel) * initial velocity

Given:
Mass of rocket (m1) = 4.40 kg
Mass of fuel (m2) = 0.053 kg
Initial velocity (v1) = 0 m/s (since the rocket is at rest initially)

Initial momentum = (4.40 kg + 0.053 kg) * 0 m/s
Initial momentum = 4.453 kg * 0 m/s
Initial momentum = 0 kg*m/s

Since the rocket is initially at rest, the initial momentum is zero.

Now, let's find the final momentum of the rocket after the fuel has been expelled.

Final momentum = (mass of rocket) * final velocity

Let's assume the final velocity of the rocket is v2.

Final momentum = (4.40 kg) * v2

According to the conservation of momentum, the initial momentum should be equal to the final momentum.

0 kg*m/s = (4.40 kg) * v2

Solving for v2, we get:

v2 = 0 kg*m/s / 4.40 kg
v2 = 0 m/s

Therefore, the velocity of the rocket after the fuel has burned is 0 m/s.