A 94- astronaut and a 1200- satellite are at rest relative to the space shuttle. The astronaut pushes on the satellite, giving it a speed of 0.25 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?

Question

A 94- astronaut and a 1200- satellite are at rest relative to the space shuttle. The astronaut pushes on the satellite, giving it a speed of 0.25 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?

Answer 1

velocityastronaut= distance/(7.5min*60sec/min)

now, conservation of momentum.

1200kg*.25m/s=94kg*distance/(7.5*60sec)

solve for distance.

YOu did not put units on numbers in your problem statement. In the Physical sciences, numerals are meaningless without units.

Answer 2

To solve this problem, we can use the principle of conservation of momentum. The initial momentum of the system is equal to the final momentum of the system.

Let's break down the problem into two parts: the astronaut and the satellite.

1. Momentum of the astronaut (before pushing the satellite):
The astronaut's initial momentum is given by the product of the mass and velocity:
Momentum = mass * velocity = (94 kg) * 0 m/s = 0 kg·m/s

2. Momentum of the satellite (after being pushed by the astronaut):
The final momentum of the satellite is also given by the mass and velocity:
Momentum = mass * velocity = (1200 kg) * (0.25 m/s) = 300 kg·m/s

Now, let's consider the combined momentum after the astronaut comes into contact with the shuttle. Since there is no external force acting on the system, the total momentum before and after the astronaut pushes the satellite must be the same.

Total initial momentum = Total final momentum

0 kg·m/s + 0 kg·m/s = 0 kg·m/s + 300 kg·m/s

Therefore, the total final momentum is 300 kg·m/s.

Now, let's solve for the initial distance from the shuttle to the astronaut. We know that the shuttle comes into contact with the astronaut 7.5 seconds after the satellite is pushed.

Using the formula for momentum:

Momentum = mass * velocity

We know that the mass and velocity of the astronaut together determine the momentum. Therefore, we can calculate the velocity of the astronaut by rearranging the equation and solving for velocity:

Velocity = Momentum / mass = 300 kg·m/s / 94 kg ≈ 3.19 m/s

Now, let's calculate the distance using the equation:

Distance = Velocity * Time

Distance = 3.19 m/s * 7.5 s ≈ 23.93 meters

Therefore, the initial distance from the shuttle to the astronaut is approximately 23.93 meters.