A 120 kg astronaut (including space suit) acquires a speed of 3.00 m/s by pushing off with his legs from an 1900 kg space capsule.

What is the change in speed of the space capsule? As the reference frame, use the position of the space capsule before the push.

if the push lasts 0.43 s, what is the average force exerted on the astronaut by the space capsule?

I do not know. I am having a hard time finding how to do this.

To answer the first part of the question, we can use the principle of conservation of momentum. According to this principle, the total momentum before and after an interaction remains constant if no external forces are acting. The momentum is calculated by multiplying the mass by the velocity.

1. Calculate the initial momentum of the astronaut and space capsule system before the push:
Initial momentum = Mass of astronaut × Initial velocity of astronaut + Mass of space capsule × Initial velocity of space capsule.

The mass of the astronaut is given as 120 kg, and the initial velocity of the astronaut is not specified. So we can assume the initial velocity of the astronaut is zero, as the astronaut is initially at rest.

Initial momentum = 120 kg × 0 + 1900 kg × 0 = 0

2. Calculate the final momentum of the astronaut and space capsule system after the push:
Final momentum = Mass of astronaut × Final velocity of astronaut + Mass of space capsule × Final velocity of space capsule.

The mass of the astronaut remains 120 kg, and the final velocity of the astronaut is given as 3.00 m/s.

Final momentum = 120 kg × 3.00 m/s + 1900 kg × Final velocity of space capsule

3. Since the reference frame is the position of the space capsule, the change in speed of the space capsule is equal in magnitude but opposite in direction to the change in speed of the astronaut. So the final velocity of the space capsule is -3.00 m/s.

Final momentum = 120 kg × 3.00 m/s + 1900 kg × -3.00 m/s

4. Calculate the change in momentum:
Change in momentum = Final momentum - Initial momentum

The change in momentum will give us the change in speed of the space capsule.

5. Subtract the initial momentum from the final momentum to get the change in momentum.

Change in momentum = (120 kg × 3.00 m/s + 1900 kg × -3.00 m/s) - 0

This will give you the change in momentum of the space capsule.

To answer the second part of the question and calculate the average force exerted on the astronaut by the space capsule, we can use Newton's second law of motion. The force exerted on an object is equal to the rate of change of momentum, and the average force can be calculated by dividing the change in momentum by the time taken.

6. Calculate the average force exerted on the astronaut by the space capsule:
Average force = Change in momentum / Time

The change in momentum is calculated in step 5, and the time given is 0.43 s.

Average force = Change in momentum / 0.43 s

This will give you the average force exerted on the astronaut by the space capsule.

To find the change in speed of the space capsule, we can use the principle of conservation of momentum. According to this principle, the total momentum before the push is equal to the total momentum after the push.

To calculate the change in speed of the space capsule, we need to first calculate the initial momentum of the astronaut and the space capsule.

The initial momentum of the astronaut (including the space suit) is given by:
Initial momentum of astronaut = mass of astronaut x initial speed of astronaut

Mass of astronaut = 120 kg
Initial speed of astronaut = 0 m/s (since the astronaut is initially at rest)

Initial momentum of astronaut = 120 kg x 0 m/s = 0 kg·m/s

The initial momentum of the space capsule is given by:
Initial momentum of space capsule = mass of space capsule x initial speed of space capsule

Mass of space capsule = 1900 kg
Initial speed of space capsule = 0 m/s (since the space capsule is initially at rest)

Initial momentum of space capsule = 1900 kg x 0 m/s = 0 kg·m/s

Since the total initial momentum is equal to zero, the total final momentum must also be zero.

The final momentum of the astronaut is given by:
Final momentum of astronaut = mass of astronaut x final speed of astronaut

Mass of astronaut = 120 kg
Final speed of astronaut = 3.00 m/s (as given)

Final momentum of astronaut = 120 kg x 3.00 m/s = 360 kg·m/s

The final momentum of the space capsule is given by:
Final momentum of space capsule = mass of space capsule x final speed of space capsule

Mass of space capsule = 1900 kg
Final speed of space capsule = ? (unknown)

Final momentum of space capsule = 1900 kg x unknown final speed of space capsule

Since the total final momentum is equal to zero, we can solve for the final speed of the space capsule:

1900 kg x unknown final speed of space capsule = -360 kg·m/s

Dividing both sides by 1900 kg:
unknown final speed of space capsule = -360 kg·m/s / 1900 kg

unknown final speed of space capsule = -0.1895 m/s

Therefore, the change in speed of the space capsule is -0.1895 m/s.

To find the average force exerted on the astronaut by the space capsule during the push, we can use the impulse-momentum theorem, which states that the impulse experienced by an object is equal to the change in momentum of the object.

The impulse experienced by the astronaut is given by:
Impulse = force x time

Average force exerted on the astronaut by the space capsule = impulse / time

Impulse = change in momentum of the astronaut
Change in momentum of the astronaut = final momentum of the astronaut - initial momentum of the astronaut

Final momentum of the astronaut = 360 kg·m/s (as calculated earlier)
Initial momentum of the astronaut = 0 kg·m/s (since the astronaut is initially at rest)

Change in momentum of the astronaut = 360 kg·m/s - 0 kg·m/s = 360 kg·m/s

Time = 0.43 s (as given)

Average force exerted on the astronaut by the space capsule = (360 kg·m/s) / (0.43 s)