Answer :
Final answer:
The change in speed of the space capsule is 0.1595 m/s. This is calculated using the law of conservation of momentum, considering the masses of the astronaut and capsule and the astronaut's speed.
Explanation:
The question is concerned with the conservation of momentum in a physics scenario where an astronaut is pushing off from a space capsule. According to the law of conservation of momentum, the total momentum of a closed system remains constant if no external forces are acting on it. In this case, the astronaut and the space capsule are initially at rest, and thus their combined initial momentum is zero. When the astronaut pushes off and gains a speed of 2.20 m/s, the space capsule will also acquire a velocity in the opposite direction to ensure the total momentum of the system remains zero.
To find the change in the speed of the space capsule, you can use the formula:
m_1 × v_1 = m_2 × v_2
where m_1 is the mass of the astronaut, v_1 is the velocity of the astronaut, m_2 is the mass of the space capsule, and v_2 is the velocity of the space capsule. Solving for v_2, you get
v_2 = (m_1 × v_1) / m_2
Plugging in the given values:
v_2 = (124 kg × 2.20 m/s) / 1710 kg
v_2 = 0.1595 m/s
The space capsule's change in speed is 0.1595 m/s in the direction opposite to the astronaut's push.
