A 90 kg astronaut and a 1100 kg satellite are at rest relative to the space shuttle. The astronaut pushes on the satellite, giving it a speed of 0.24 m/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?
To find the initial distance from the shuttle to the astronaut, we can use the formula for displacement:
\[ s = u \cdot t \]
Where:
- s is the displacement (distance)
- u is the initial velocity
- t is the time
In this case, the astronaut is moving towards the shuttle, so the initial velocity would be in the opposite direction with a magnitude of 0.24 m/s.
Using the formula, we have:
\[ s = (-0.24 \, \text{m/s}) \cdot (7.5 \, \text{s}) \]
Calculating the result:
\[ s = -1.8 \, \text{m} \]
The negative sign indicates that the astronaut is moving in the opposite direction of the shuttle. So, the initial distance from the shuttle to the astronaut is 1.8 meters.