Question

a 87-kg astronaut and a 1000-kg satellite are at rest relative to the space shuttle. the astronaut pushes on the satellite, giving it a speed of 0.22m/s directly away from the shuttle. seven-and-a-half seconds later the astronaut comes into contact with the shuttle. part a what was the initial distance from the shuttle to the astronaut?

Answer 1

The initial distance from the shuttle to the astronaut was approximately 18.965 meters, calculated using conservation of momentum and kinematic equations.

Step-by-step explanation:

The question involves calculating the initial distance between an astronaut and a shuttle using the concepts of conservation of momentum and kinematics in space. When the astronaut pushes the satellite, both the astronaut and the satellite experience equal and opposite forces according to Newton's third law, and thus they will have equal and opposite momenta because they start at rest relative to each other.

The astronaut's velocity can be calculated using the conservation of momentum.

The satellite's final momentum is equal to 1000 kg × 0.22 m/s, and assuming no external forces, the astronaut's momentum will be equal and opposite.

This gives the astronaut a speed of v_a = (1000 kg × 0.22 m/s) / 87 kg = 2.5287 m/s after the push.

Using the astronaut's speed v_a, and knowing that it takes 7.5 seconds to reach the shuttle, the initial distance can be found using the kinematic equation d = v × t.

Here, d = 2.5287 m/s × 7.5 s, giving an initial distance of approximately 18.965 m from the shuttle.