A 65-kg astronaut pushes against the inside back wall of a 2000kg spaceship and moves toward the front. Her speed increases from 0 to 1.6 m/s If her push lasta 0.3 seconds what is the average force that the astronaut exerts on the wall of the spaceship?? If the spaceship was initially at rest, with what speed does it recoil? What was the object of reference that you used to answer parts a and b?

a. V = Vo + a*t.

1.6 = 0 + a*0.3, a = 5.33 m/s^2.

F = M*a = 65 * 5.33 = 346.7 N.

Avergae Force=Impluse/time

Impulse=m(vf-vi) so 65(1.6)
Impulse=104
Average Force=104/.3 which is 346.67 N
(This is another way)

2nd part is asking for velocity not acceleration

Well, it seems like that astronaut really wanted to get to the front of the spaceship in a hurry! Let's see what we can calculate here.

To find the average force that the astronaut exerts on the wall of the spaceship, we can use Newton's second law, which states that force equals mass times acceleration (F = ma).

The change in momentum (Δp) of the astronaut can be calculated by multiplying the astronaut's mass (m) by her change in velocity (Δv): Δp = mΔv.

The average force (F_avg) exerted on the wall can be found by dividing the change in momentum by the time interval (Δt) of the push: F_avg = Δp / Δt.

Given that the astronaut's mass (m) is 65 kg, her change in velocity (Δv) is 1.6 m/s, and the push lasted for 0.3 seconds, we can plug these values into the equation to find the average force:

F_avg = (65 kg) * (1.6 m/s) / (0.3 s)

Calculating this, we find that the average force exerted on the wall of the spaceship is approximately 346.67 Newtons.

Now, let's move on to the speed with which the spaceship recoils. Since momentum is conserved in this isolated system, the change in momentum of the astronaut must be equal in magnitude but opposite in direction to the momentum change of the spaceship.

The momentum (p) of the spaceship can be calculated using the equation p = mv, where m is the spaceship's mass and v is its velocity.

Initially, the spaceship is at rest, so its initial momentum is zero. After the push, the astronaut has a momentum of (65 kg) * (1.6 m/s) and is moving in the opposite direction.

The final momentum of the spaceship must be equal in magnitude but opposite in direction, so we can set up the equation:

(65 kg) * (1.6 m/s) = (2000 kg) * (v)

Solving for v, we find that the spaceship recoils with a speed of approximately 0.052 m/s.

Now, regarding the object of reference, I used Newton's laws of motion and momentum conservation principles to answer parts a and b. The reference frame is the spaceship itself, as we are analyzing the forces and momentum within the spaceship's frame of reference.

Hope that brings a smile to your face!

To find the average force the astronaut exerts on the wall of the spaceship, we can use Newton's second law of motion, which states that the force is equal to the change in momentum divided by the time interval.

Step 1: Calculate the momentum of the astronaut initially and after the push.
The momentum of an object is given by the formula: momentum = mass × velocity.

Initial momentum of the astronaut (before the push):
p1 = mass × velocity = 65 kg × 0 m/s = 0 kg m/s

Final momentum of the astronaut (after the push):
p2 = mass × velocity = 65 kg × 1.6 m/s = 104 kg m/s

Step 2: Calculate the change in momentum.
Δp = p2 - p1 = 104 kg m/s - 0 kg m/s = 104 kg m/s

Step 3: Calculate the average force.
Force = Δp / time interval = 104 kg m/s / 0.3 s = 346.67 N

Therefore, the average force that the astronaut exerts on the wall of the spaceship is 346.67 N.

Regarding part b of your question, the recoil speed of the spaceship can be determined by using the principle of conservation of momentum. Since the astronaut's push is the only external force acting on the spaceship-astronaut system, the total momentum before and after the push must be conserved.

Step 1: Calculate the initial momentum of the spaceship.
Initial momentum of the spaceship (before the push):
p_ship1 = mass_ship × velocity_ship = 2000 kg × 0 m/s = 0 kg m/s

Step 2: Calculate the final momentum of the spaceship.
Final momentum of the spaceship (after the push):
p_ship2 = mass_ship × velocity_ship

Since the total momentum is conserved, we can set it equal to the astronaut's final momentum:
p_ship2 = p2 = 104 kg m/s

Step 3: Solve for the velocity of the spaceship.
velocity_ship = p_ship2 / mass_ship = 104 kg m/s / 2000 kg

Calculating this will give you the recoil speed of the spaceship.