A 92kg astronaut and a 1.2E3kg satellite are at rest relative to the space shuttle. The astronaut pushes on the satellite, giving a speed of 0.14m/s directly away from the shuttle. Seven and a half seconds later the astronaut comes into contact with the shuttle. What was the initial distance from the shuttle to the astronaut?

Conservation of momentum applies. You knwo the momentum of the satellite (mv), so the momentum of the man is the same. Calculate his velocity, then distance from distance= velocity*time

To find the initial distance from the shuttle to the astronaut, we can use the concept of conservation of momentum.

The momentum of an object is given by the product of its mass and velocity: momentum = mass x velocity.

Given that the mass of the astronaut is 92 kg and the mass of the satellite is 1.2E3 kg (1.2 x 10^3 kg), we can calculate the momentum of the satellite.

Momentum of satellite = mass of satellite x velocity of satellite = (1.2E3 kg) x (0.14 m/s) = 168 kgm/s

According to the conservation of momentum, the momentum of the astronaut should also be 168 kgm/s.

Momentum of astronaut = mass of astronaut x velocity of astronaut

Rearranging the equation, we can solve for the velocity of the astronaut:

Velocity of astronaut = momentum of astronaut / mass of astronaut = (168 kgm/s) / (92 kg) = 1.826 m/s (rounded to 3 decimal places)

Now that we have the velocity of the astronaut, we can calculate the initial distance from the shuttle to the astronaut using the formula:

Distance = velocity x time

Given that the time taken is 7.5 seconds, we can substitute the values to find the initial distance:

Distance = (1.826 m/s) x (7.5 s) = 13.695 m (rounded to 3 decimal places)

Therefore, the initial distance from the shuttle to the astronaut is approximately 13.695 meters.