An 95.0 kg astronaut is working on the engines of a spaceship that is drifting through space with a constant velocity. The astronaut turns away to look at Earth and several seconds later is 26.3 m behind the ship, at rest relative to the spaceship. The only way to return to the ship without a thruster is to throw a wrench directly away from the ship. If the wrench has a mass of 0.530 kg, and the astronaut throws the wrench with a speed of 18.0 m/s, how long does it take the astronaut to reach the ship?

work in inertial coordinate system of spaceship

.530*18 = 95 v conservation of momentum
v = .530*18/95

t = 26.3/v

To find the time it takes for the astronaut to reach the ship, we need to calculate the time it takes for the wrench to reach the ship, and then consider the time it would take for the astronaut to cover the same distance.

First, let's find the initial velocity of the astronaut when he throws the wrench. Since the astronaut is at rest relative to the spaceship, his initial velocity is zero.

Next, let's find the relative velocity of the wrench with respect to the spaceship. The relative velocity is the difference between the wrench's velocity and the spaceship's velocity.

The wrench's velocity is given as 18.0 m/s away from the ship. Since the spaceship is drifting with a constant velocity, we can assume its velocity is also constant and equal to the velocity at which the astronaut is moving away from it when he throws the wrench. This means the spaceship's velocity is also 18.0 m/s away from the ship.

The relative velocity of the wrench with respect to the spaceship is then:

Relative velocity = Wrench's velocity - Spaceship's velocity
= 18.0 m/s - 18.0 m/s
= 0 m/s

This means the wrench is not moving relative to the spaceship after it is thrown.

Since the wrench is not moving relative to the spaceship, it will take an infinite amount of time for the wrench to reach the ship. In other words, the wrench will never reach the ship.

Therefore, the astronaut can never reach the ship by throwing the wrench alone. The only way for the astronaut to reach the ship is to use a thruster or some other means of propulsion.