An astronaut on a space walk bumps the shuttle and starts moving away at a velocity of 0.02m/s. The astronauts mass is 100kg. He has takes a 1kg "safety week" and shoves it away in exactly the direction of his motion at a speed of 6m/s. What speed does the astronaut move back toward the space shuttle?

Question

An astronaut on a space walk bumps the shuttle and starts moving away at a velocity of 0.02m/s. The astronauts mass is 100kg. He has takes a 1kg "safety week" and shoves it away in exactly the direction of his motion at a speed of 6m/s. What speed does the astronaut move back toward the space shuttle?

Answer 1

conservation of momentum

initial momentum=sum final momentums
100(-0.02)=1(6)+99(V) solve for V.

Answer 2

what is the final answer? :(

Answer 3

To solve this problem, we can use the principle of conservation of momentum. The total momentum before the astronaut shoves the "safety weight" away is equal to the total momentum after the shove.

Given:
Mass of the astronaut (m1) = 100 kg,
Mass of the safety weight (m2) = 1 kg,
Initial velocity of the astronaut (v1_initial) = 0.02 m/s,
Velocity of the safety weight (v2_initial) = 6 m/s.

We can find the final velocity of the astronaut (v1_final) using the conservation of momentum equation:

(m1 * v1_initial) + (m2 * v2_initial) = (m1 * v1_final) + (m2 * v2_final)

Now we can substitute the given values into the equation:

(100 kg * 0.02 m/s) + (1 kg * 6 m/s) = (100 kg * v1_final) + (1 kg * v2_final)

(2 kg·m/s) + (6 kg·m/s) = (100 kg * v1_final) + (1 kg * v2_final)

8 kg·m/s = (100 kg * v1_final) + (1 kg * v2_final)

Since the safety weight was pushed away in the same direction as the astronaut's motion, the velocity of the safety weight (v2_final) will be negative.

Let's assume the astronaut's final velocity (v1_final) is in the opposite direction to his initial motion, and under this assumption, the safety weight's final velocity (v2_final) will be positive.

Rewriting the equation:

8 kg·m/s = (100 kg * v1_final) - (1 kg * v2_final)

We need to determine the value of v1_final, so let's solve for it:

100 kg * v1_final = 8 kg·m/s + (1 kg * v2_final)

v1_final = (8 kg·m/s + (1 kg * v2_final)) / 100 kg

Now we need to substitute the known values for v2_final into the equation and calculate v1_final:

If the safety weight had been pushed away at 6 m/s in the same direction as the astronaut's motion, then v2_final = -6 m/s.

v1_final = (8 kg·m/s + (1 kg * -6 m/s)) / 100 kg

v1_final = (8 kg·m/s - 6 kg·m/s) / 100 kg

v1_final = 2 kg·m/s / 100 kg

v1_final = 0.02 m/s

Therefore, the astronaut moves back towards the space shuttle at a speed of 0.02 m/s.