Please help me, thank you.
A 100 kg astronaut is standing on the outside surface of a 4.50 x 10^4 kg spacecraft. The astronaut jumps away from the spacecraft at 8.00 m/s. What happens to the spacecraft?
multiply (simplified fraction)
-8/3*(7/1)
that's not right can someone please help.
I believe this is a case of conservation of momentums, namely zero since both objects were stationary to start with.
M1V1 + M2V2 = 0
100*8 + 45000*V2 = 0
V2
= -100*8/45000
= -0.0178 m/s.
Answer: The spaceship moves at 0.0178 in the opposite direction as the astronaut.
Erratum:
Answer: The spaceship moves at 0.0178 m/s in the opposite direction as the astronaut.
To understand what happens to the spacecraft, we need to apply Newton's third law of motion, which states that "for every action, there is an equal and opposite reaction."
When the astronaut jumps away from the spacecraft, they exert a force on the spacecraft, and the spacecraft exerts an equal and opposite force on the astronaut.
Let's first calculate the momentum of the astronaut's jump. The momentum (p) of an object is calculated as the product of its mass (m) and its velocity (v):
Momentum = mass × velocity
Given:
Mass of the astronaut (m1) = 100 kg
Velocity of the astronaut (v1) = 8.00 m/s
Momentum of the astronaut's jump (p1) = m1 × v1
Substituting the values:
p1 = 100 kg × 8.00 m/s
p1 = 800 kg·m/s
Now, according to Newton's third law, the momentum gained by the astronaut (p1) will be equal and opposite to the momentum gained by the spacecraft (p2).
p1 = -p2 (since the direction is opposite)
Thus, p2 = -800 kg·m/s
The negative sign indicates that the spacecraft gains momentum in the opposite direction to the astronaut's jump.
Since momentum is the product of mass and velocity, we can rearrange the equation to solve for the spacecraft's velocity (v2):
p2 = m2 × v2
Where:
Mass of the spacecraft (m2) = 4.50 × 10^4 kg
Substituting the values:
-800 kg·m/s = (4.50 × 10^4 kg) × v2
Now we can solve for v2:
v2 = -800 kg·m/s / (4.50 × 10^4 kg)
v2 ≈ -0.0178 m/s
The negative sign indicates that the spacecraft moves in the opposite direction to the astronaut's jump.
Therefore, the spacecraft moves away from the astronaut at approximately 0.0178 m/s (relative to the initial velocity of the spacecraft).